In this paper the analysis of the classical dynamics of a charged particle is carried out without considering that the electromagnetic field necessarily goes to zero at infinity. A quite general non-linear equation of motion is obtained for an extended charged particle valid for any distribution of charge in the particle and for an electromagnetic field satisfying any boundary conditions. Some common approximations are analyzed with detail to determine how the usual difficulties arise.

A model of the extended classical charged particle is developed further to prove that the electron potential can be expressed as a superposition of null waves. The null waves are solutions of the homogeneous wave equation and are related to some recently discovered types of solutions which are localized and propagate without dispersion. Connections with quantum electrodynamics and the fine structure constant are indicated.

A theory of the extended classical charged particle is presented. The theory assumes extension along the forward light cone of the particle instead of the usual now-plane. Solutions are given for many of the traditional problems including 4/3, instability, infinite self-energy, and runaway velocity. The Lorentz and Lorentz-Dirac equations are derived from a more general equation of motion.

A coordinate-free formulation is established for (semi) classical particle-field interactions. The exterior language of spacetime chains and De-Rham currents enables the description to include extended strings and membranes besides point particles. Treating physical fields in terms of sections of particular bundles, a unified account of interactions is presented in terms of an intrinsic action principle on a bundle of jets over spacetime. The theory is illustrated by considering the specific model of point particles with intrinsic spin covariantly coupled (...) to theU(1) andSL(2, C) connections describing the electromagnetic and gravitational fields, respectively. The notion of dual spin is examined in this context and coupled equations for this particle-field system are explicitly derived in a local chart. Attention is drawn to the global implications of the theory. (shrink)

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding (...) coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed. (shrink)

Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior (...) because the true physical mass still obeys M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. A Born’s Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 GeV, we find a value for the magnitude $|\mathcal{M } | = 119.7\mbox{~MeV}$ that, coincidentally, is close to the mass of the muon m μ =105.7 MeV. (shrink)

It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential Aα—interpreted absolutely as a measure of the local shift of each particle off its (...) mass shell—rather than theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance. (shrink)

Theories of free fields describing spin zero and1/2 extended particles are derived within the stochastic quantum field theory (SQFT) framework. Covariant SQFT analogs of free Schwinger functions and Feynman propagators are obtained, and explicit expressions for charge and four-momentum operators are derived which exhibit a remarkable formal resemblance to their local counterparts. It is shown that the essential results of the LSZ formalism for interacting fields also have their counterpart in SQFT, and that the same holds true of Wightman's (...) reconstruction theorem. Fields on quantum space-time do not obey the local (anti)-commutativity postulate, but we argue that due to the uncertainty principle this postulate cannot be operationally justified as an expression of microcausality despite the customary identification of the two notions. An operationally consistent microcausality condition is proposed instead. (shrink)

Complexified Liénard–Wiechert potentials simplify the mathematics of Kerr–Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr–Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be (...) multi-valued. A generalized analytic continuation is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr–Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

Considering only exchange forces, the binding energies and excited states of nuclei up to 24 Mg are predicted to within charge independence, and there is no reason why the model should not be extended to cover all of the elements. A comparison of theory with experiment shows that the energy of one exchange is 2.56 MeV. Moreover, there is an attractive well of depth 30 MeV, corresponding to the helium nucleus, before exchange forces become operative. A possible explanation of (...) the origin of mesons is also presented. (shrink)

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment (...) by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed. (shrink)

The use of charged-particle radiation therapy is an increasingly important development in the treatment of cancer. One of the most pressing controversies about the use of this technology is whether randomised controlled trials are required before this form of treatment can be considered to be the treatment of choice for a wide range of indications. Equipoise is the key ethical concept in determining which research studies are justified. However, there is a good deal of disagreement about how this (...) concept is best understood and applied in the specific case of CPRT. This report is a position statement on these controversies that arises out of a workshop held at Wolfson College, Oxford in August 2011. The workshop brought together international leaders in the relevant fields , including proponents on both sides of the debate, in order to make significant progress on the ethical issues associated with CPRT research. This position statement provides an ethical platform for future research and should enable further work to be done in developing international coordinated programmes of research. (shrink)

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode (...) fields of the 0, 1, 2, 3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Abraham–Lorentz–Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed. (shrink)

In August 2011, a group of medical doctors, ethicists, academic and medical physicists were asked to debate and reach consensus on the potential need for randomised control trials to test charged particle radiation therapy for treating tumours. The outcome of the meeting was a paper recently published in the Journal of Medical Ethics entitled “Position statement on ethics, equipoise and research on charged particle therapy” by Sheehan et al. However 6 of the 30 meeting participants withdrew (...) from authorship of the ‘position statement’ because their views were not adequately represented. The ‘position statement’ did not state our reasons for withdrawing from the statement, which is a considerable omission. We had two principal objections: the case for the benefits to patients and society of randomized trials to test CPRT was not adequately represented, and the complexities and potential harms of CPRT were not clearly stated. In this response we explain and justify our objections. Patients, doctors and policymakers seeking to make independent judgments about whether equipoise exists for the relative benefits of CPRT should therefore read this document alongside the ‘position’ statement. (shrink)

Examining the process of action at a distance, we arrive at the following conclusions: (a) The virtual photons and mesons transmitting Coulomb and nuclear forces, respectively, do not arise from “temporary violations of energy conservation,” but, on the contrary, exactly embody the potential energy corresponding to the relevant forceF that they transmit on their collision with the charged particles or nucleons via the formula Δp=FΔt. (b) In the case of an attractive force, the energy of these photons and mesons (...) is negative. The way this comes about is made clear by a more detailed investigation of Feynman's notion of “traveling backward in time.” (c) The action corresponding to, e.g., a virtual photon's appearance is exactly one quantumh, which fact is responsible for the unobservability of such photons. Some consequences of the revised conception of potential energy for, e.g., the tunnel and the Bohm-Aharonov effect are mentioned. (shrink)

In this paper—dedicated to Prof. Asim O. Barut—we generalize the Diracnon-linear electrodynamics by introducing two potentials(namely, the vector potential A and the pseudo-vector potential γ5B of the electromagnetic theorywith charges and magnetic monopoles) and by imposing the pseudoscalar part of the product ωω* to be zero, with ω≡A+γ5B. We show that the field equations of such a theory possess a soliton-like solution which can representa priori a “charged particle,” since it is endowed with a Coulomb field plus the (...) field of a magneticdipole. The rest energy of the soliton is finite, and the angular momentum stored in its electromagnetic field can be identified—for suitable choices of the parameters—with the spin of the charged particle. Thus, this approach seems to yield a classical model for the charged (spinning) particle which does not encounter the problems met by earlier attempts in the same direction. (shrink)

In the seminal works from Santos and Gozalo and Marletto and Vedral, it is shown how the Aharonov–Bohm effect can be described as the result of an exchange of virtual photons between the solenoid and the quantum charged particle along its propagation through the interferometer, where both the particle and the solenoid interact locally with the quantum electromagnetic field. This interaction results in a local and gauge-independent phase generation for the particle propagation in each path of (...) the interferometer. Here we improve the cited treatments by using the quantum electrodynamics formalism in the Lorentz gauge, with a manifestly gauge-independent Hamiltonian for the interaction and the presence of virtual longitudinal photons. Only with this more complete and gauge-independent treatment it is possible to justify the acquired phases for interferometers with arbitrary geometries. We also extend the results to the electric version of the Aharonov–Bohm effect. Finally, we propose an experiment that could test the locality of the Aharonov–Bohm phase generation. (shrink)

It is shown in the present paper that the transformation relating a parallel transported vector in a Weyl space to the original one is the product of a multiplicative gauge transformation and a proper orthochronous Lorentz transformation. Such a Lorentz transformation admits a spinor representation, which is obtained and used to deduce the transportation properties of a Weyl spinor, which are then expressed in terms of a composite gauge group defined as the product of a multiplicative gauge group and the (...) spinor group. These properties render a spinor amenable to its treatment as a particle coupled to a multidimensional gauge field in the framework of the Kaluza–Klein formulation extended to multidimensional gauge fields. In this framework, a fiber bundle is constructed with a horizontal, base space and a vertical, gauge space, which is a Lie group manifold, termed its structure group. For the present, the base is the Minkowski spacetime and the vertical space is the composite gauge group mentioned above. The fiber bundle is equipped with a Riemannian structure, which is used to obtain the classical description of motion of a spinor. In its classical picture, a Weyl spinor is found to behave as a spinning charged particle in translational motion. The corresponding quantum description is deduced from the Klein–Gordon equation in the Riemann spaces obtained by the methods of path-integration. This equation in the present fiber bundle reduces to the equation for a Weyl spinor, which is close to but differs somewhat from the squared Dirac equation. (shrink)

High-spin states in the odd-odd N = Z nucleus Co-54 have been investigated by the fusion-evaporation reaction Si-28(S-32,1 alpha 1p1n)Co-54. Gamma-ray information gathered with the Ge detector array Gammasphere was correlated with evaporated particles detected in the charged particle detector system Microball and a 1 pi neutron detector array. A significantly extended excitation scheme of Co-54 is presented, which includes a candidate for the isospin T = 1, 6(+) state of the 1f(7/2)(-2) multiplet. The results are compared (...) to large-scale shell-model calculations in the fp shell. Effective interactions with and without isospin-breaking terms have been used to probe isospin symmetry and isospin mixing. A quest for deformed high-spin rotational cascades proved negative. This feature is discussed by means of cranking calculations. (shrink)

The project of chemistry to classify substances and develop techniques for their transformation into other substances rests on assumptions about the means by which compounds are constituted and reconstituted. Robert Boyle not only proposed empirical tests for a metaphysics of material corpuscules, but also a principle for designing experimental procedures in line with that metaphysics. Later chemists added activity concepts to the repertoire. The logic of activity explanations in modern times involves hierarchies of activity concepts, transitions between levels through non-dispositional (...) groundings. Such hierarchies terminate in powerful particulars, such as elementary charged particles. Do these have a fundamental place in the most recent accounts of molecular architecture, stabilities and transformations? However, a close study of the contemporary chemistry of substances transforming reactions discloses a hybrid metaphysics, making use of both the Boylean corpuscles and Faradayan fields. This is illustrated by an analysis of the metaphysics inherent in John Polanyi’s use of “chemoluminescence” to follow the formation of products in chemical reactions. A brief sketch of a resolution of the tension between the two metaphysical schemes is drawn from Niels Bohr’s radical metaphysics extended from the quantum realm proper to chemistry (and perhaps beyond). (shrink)

A generalization of gauge theory in which the gauge potential1-form is replaced by a p-form is studied. Charged particles are then replaced by elementary extended objects of dimension p−1. It is shown that this extension is compatible with space-time locality only if the gauge group is U(1). A source which is a closed p−1 surface has zero total charge and corresponds to a particle-antiparticle pair. Its quantum rate of production in an external uniform field is evaluated semiclassically. (...) The analog of the Dirac magnetic pole is constructed. It is another extended object, of dimension n−p−3, where n is the dimension of space-time. The “electric” and “magnetic” charges obey the Dirac quantization condition. This condition is derived in two different ways. One method makes use of local gauge patches and the other brings in singular gauge transformations. A topological mass term is introduced and it is shown that it can coexist with a magnetic pole when n=2p+1, provided the topological mass is quantized. (shrink)

The extended dual-aspect monism framework of consciousness, based on neuroscience, consists of five components: (1) dual-aspect primal entities; (2) neural-Darwinism: co-evolution and co-development of subjective experiences (SEs) and associated neural-nets from the mental aspect (that carries the SEs/proto-experiences (PEs) in superposed and unexpressed form) and the material aspect (mass, charge, spin and space-time) of fundamental entities (elementary particles), respectively and co-tuning via sensorimotor interaction; (3) matching and selection processes: interaction of two modes, namely, (a) the non-tilde mode that is (...) the material and mental aspect of cognition (memory and attention) related feedback signals in a neural-network, which is the cognitive nearest past approaching towards present; and (b) the tilde mode that is the material and mental aspect of the feed forward signals due to external environmental input and internal endogenous input, which is the nearest future approaching towards present and is a entropy-reversed representation of non-tilde mode; (4) the segregation and integration of information, and (5) the necessary ingredients of SEs (such as wakefulness, attention, re-entry, working memory, stimulus at or above threshold level, and neural-net PEs). This framework leads to structural and functional coherence between the mind and the brain, bridges the explanatory gap (the gap between SEs and their neural-correlates), and leads to our mundane subjective experiences. This extended dual-aspect monism (eDAM) framework (Vimal, 2008, 2010, 2013, 2015a, 2015b) could be the fundamental basis of various religions and philosophies. This is a Western perspective. On the other hand, Eastern perspectives emphasize the practical methods for achieving altered experience at samadhi state. An important corollary of these methods (such as yogic method) is the sublimation of negative aspects of seven groups of self-protective energy system (desire, anger, ego, greed, attachment, jealousy, and selfish-love) into their positive aspects. Their negative aspects create war and suffering, whereas their positive aspects advance science and technology, family values, peace, and happiness. Here, the Western perspective framework is extended to include the concepts of the sublimation process to encompass Eastern perspectives. The four elements (war, suffering, peace, and happiness) are ubiquitous in both space and time because they are essential contributors to the variations for natural selection in our evolutionary system. The sublimation process optimizes the system: minimizes war and suffering, maximizes peace and happiness, and enhances family values and individual progress. This is consistent with both Eastern and Western perspectives. (shrink)

A new scheme is proposed in order to deduce an equation of motion for a spinless charged point particle leading to an equivalent Landau–Lifshitz equation of motion. Consequently Larmor’s formula must be substituted by a new expression for the large distance radiation rate of energy. A constraint appears on the applicability of the Maxwell electromagnetic tensor. The particular case of a sudden force is analyzed in order to show the physical results predicted by the new model. A geometrical (...) rearrangement of the energy explains the balance. (shrink)

We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.In 2+1 dimensional spacetime, a velocity of the particle and spin tensor are dependent to each other and the chirality (...) can not be introduced. The free particle has 7 constants of motion: The momentum three vector, the charge, the energy in proper time, the scalar constant spin or magnetic polarization and the two components of total angular momentum. Two component electric polarizations oscillate with Zitterbewegung frequency.In 1+1 dimensional spacetime we have an independent velocity vector and a scalar spin tensor. The free particle has 5 integrals of motion: The momentum two vector, the charge, the energy in proper time, and the scalar total angular momentum. The normal component of the velocity or the scalar electric polarization oscillates with Zitterbewegung frequency.In 3+1 dimensional spacetime, the particle has an independent velocity vector, spin tensor and chirality. The free particle has 12 integrals of motion: The momentum four vector, the charge, the energy in proper time or mass, the three vector spin or magnetic polarizations and three components of total angular momentum. The parallel component of velocity into momentum and the normal components of the spin tensor or the spin three vector are constants of motion for the free particle. The chirality and electric polarizations oscillate with the Zitterbewegung frequency. The system is superintegrable in all dimensions. (shrink)

Studying astroparticle physics sheds new light on scientific explanation and on the ways in which cosmology is empirically underdetermined or not. Astroparticle physics extends the empirical domain of cosmology from purely astronomical data to “multi-messenger astrophysics”, i.e., measurements of all kinds of cosmic rays including very high energetic gamma rays, neutrinos, and charged particles. My paper investigates the ways in which these measurements contribute to cosmology and compares them with philosophical views about scientific explanation, the relation between theory and (...) data, and scientific realism. The “standard models” of cosmology and particle physics lack of unified foundations. Both are “piecemeal physics” in Cartwright's sense, but contrary to her metaphysics of a “dappled world” the work in both fields of research aims at unification. Cosmology proceeds “top-down”, from models to data and from large scale to small-scale structures of the universe. Astroparticle physics proceeds “bottom-up”, from data taking to models and from subatomic particles to large-scale structures of the universe. In order to reconstruct the causal stories of cosmic rays and the nature of their sources, several pragmatic unifying strategies are employed. Standard views about scientific explanation and scientific realism do not cope with these “bottom-up” strategies and the way in which they contribute to cosmology. In addition it has to be noted that the shift to “multi-messenger astrophysics” transforms the relation between cosmological theory and astrophysical data in a mutually holistic way. (shrink)

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → (...) 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results. (shrink)

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.

A geometro-differential quantum theory of extended particles is presented. The geometrical selling is that of Hilbert fiber bundles whose base manifolds are pseudo-Riemannian space-times of points χ which are interpreted as partial aspects of physical reality (the extended particle). The fibers are carrier spaces of induced (internal configuration and momentum) representations of the structural group (the de Sitter group here). Sections of these bundles are seen as physical representations of the particle, and their values in the (...) fibers are interpreted as states of internally localized modes composing the particle. This geometrical structure is “analogous” to that of a geometro-stochastic quantization developed in recent years. The physical interpretation is a combination of those of an old functional quantum theory and of an induced representation scheme based on an interpretation of intertwining, between configuration and momentum representations, as localization, materialization, and propagation of particles. Our model is applied in two cases: (1) Induced representation is applied in both space-time and internal space: both have de Sitter symmetry whose connection is ignored. Intertwining is considered in both spaces in a composed fashion. (2) For generic spacetimes and when the connection is taken into account, intertwining is applied only in the internal space. Parallel transport is combined with intertwining for a redefinition of localization, materialization, and propagation (the latter in a path integral context inspired from geometro-stochastic quantization). (shrink)

The semigroup of trajectories in Minkowski space-time and its induced representations are constructed as a generalization of the Galilei case. They describe relativistic pointlike particles and yield the free propagator as a path integral in the space of trajectories parametrized by a fifth parameter. This non physical propagator in a five-dimensional space is integrated over the fifth parameter to yield the physical propagator in Minkowski space. Thereafter, this notion is applied to a model of extended particles with internal Poincaré (...) symmetry and moving in an external Minkowski space. The geometrical structure is of Hilbert bundles and the interaction is introduced as a connection. The propagator is a path integral with respect to either the internal and external trajectories and reduces to a product of an internal and an external propagator when the interaction is ignored, just as has been found in a previous work with representations of the group rather than those of the semigroup. (shrink)

With the widespread application of electric vehicles, the study of the power lithium-ion battery has broad prospects and great academic significance. The state of charge is one of the key parts in battery management system, which is used to provide guarantee for the safe and efficient operation of LIB. To obtain the reliable SOC estimation result under the influence of simple model and measurement noise, a novel estimation method with adaptive feedback compensator is presented in this paper. The simplified dynamic (...) external electrical characteristic of LIB is represented by the one-order Thevenin equivalent circuit model and then the ECM parameters are identified by the forgetting factor recursive least squares method. Fully taking into account the feedback effect of terminal voltage innovation, the combination of adaptive extended Kalman filter and innovation vector-based proportional-integral-derivative feedback is proposed to estimate the LIB SOC. The common single proportional feedback of Kalman filter is replaced by the innovation vector-based PID feedback, which means that the multiple prior terminal voltage innovation is used in the measurement correction step of KF. The results reveal that the AEKF with PID feedback compensation strategy can improve the SOC estimation performance compared with the common AEKF, and it reveals good robust capability and rapid convergence speed for initial SOC errors. The maximum absolute error and average absolute error for SOC estimation are close to 4% and 2.6%, respectively. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered flat-space case, the (...) fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables ξ, a physical wave Ψ x (ξ) representing the proper characteristics of the particles, and a functional wave X [ Ψ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The first (...) study is undertaken in a special instance Ψ x (ξ) = ξ(x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed. (shrink)

Along the lines of a previous work, the geometrical structure of Hibert bundles describing extended quantum free particles is repeated with Galilei external and internal independent symmetries. Then, in order to introduce the interaction, this structure is extended by replacing configuration and momentum spaces by the socelled spaces of trajectories and extended velocity boosts, respectively. These provide representations giving the probability amplitudes for the particle to follow certain trajectories. The interaction can be introduced in the transformation (...) law from functions on the space of trajectories (free dynamics) to functions on spacetime (intracting dynamics). This transformation law, which makes use of a universal distribution, is seen as a functional in our work according to a quantum functional theory which generalizes the ideas of de Broglie. Intertwining of induced representations gives the free propagator in the space of trajectories and, henceforth, the propagator with interaction in space-time for the extended particle. (shrink)

In this letter we demonstrate that the fermionic zero modes on a superconducting domain wall can be associated to an one dimensional \ supersymmetry that contains non-trivial topological charges. In addition, the system also possesses three distinct \ supersymmetries with non-trivial topological charges and we also study some duality transformations of the supersymmetric algebras.

Consideration of the velocity-field momentum of an accelerating charged particle leads to an explanation of the Schott force accompanying the radiation reaction.

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: [email protected] , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected] . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: [email protected]. (shrink)

This article compares treatments of the Stern–Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector but we cannot explain why there are only two locations where the electron is ever found. Using non-relativistic or relativistic quantum mechanics, (...) we can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum but we cannot explain another feature that could be explained within any of the other theories. (shrink)

A classical model of an elementary particle is considered in the framework of the bimetric general relativity theory. The particle is regarded as a spherically symmetric object filling its Schwarzschild sphere and made of matter having mass density, pressure, and charge density. The mass is taken to be the Planck mass, and possible values of the charge are taken as zero, ±1/3e, ±2/3e, and ±e, with e the electron charge.

Some problems relating to the probabilistic description of a free particle and of a charged particle moving in an electromagnetic field are discussed. A critical analysis of the Klein-Gordon equation and of the Dirac equation is given. It is also shown that there is no connection between commutativity of operators for physical quantities and the existence of their joint probability. It is demonstrated that the Heisenberg uncertainty relation is not universal and explained why this is so. A (...) universal uncertainty relation for canonically conjugate coordinates and momenta is suggested. (shrink)

There is a process that starts from the Lagrangian of a set of field equations and leads to a spectrum of particle states. The process is applied in this article to a Lagrangian for the Dirac equation. It leads to a differential equation with solutions that describe particles with definite mass, angular momentum J, charge, and isotopic spin I, having I = J. There is no suggestion of strangeness. The theory is in rough agreement with the masses of many (...) of the 0+ (0–+) and 0+ (0++) mesons and with the masses of the nonstrange 1/2 (1/2+) and 3/2 (3/2+) baryons. (shrink)