Barut's classical model of the spinning particle having external dynamical variables x and p and internal dynamical variables $\bar z$ and z is taken into account. The path integrations over holomorphic spinors $\bar z$ and z are discussed. This quantization gives the kernel of the relativistic particles with higher spin as well as the Dirac electron. The Green's function of the spin-n/2 particle is obtained.

Rotations in Quantum Mechanics are a very well-known subject. When one is faced with rotations related to the SO group, for instance, all the underlying operators are well-known and built from their classical counterparts. However, when it comes to represent rotations related to the SU group, it is always argued that there is no classical counterpart from which the expressions for the quantum mechanical operators can be built. The approach is always done using matrix representation. In the way of this (...) aproach, one assumes that the operators related to SU are pseudovectors and end up with the weird result that only rotations by multiples of \ would bring the system to its original situation. In Olavo we have shown that any half-integral spin system can be represented in the Schrödinger picture by solving a Schrödinger equation with well defined expressions for the SU differential operators. It turned out that two of these operators are symmetric tensors, not pseudovectors or antisymmetric tensors. In this paper we use these results to dismiss with the \ conundrum. (shrink)

A theoretical and experimental search for the so-called Weyssenhof behavior of a spinning particle, due to the noncollinearity of its velocity and momentum, has been undertaken. Z-independent solutions of Maxwell's equations had previously been produced with a nonzeros z component of the Poynting vector; indeed, Imbert emphasized that the spatial exponential damping of Fresnel's evanescent wave would entail a nonzero value for the integral ε εs z dx dy. Excellent experimental verifications of this point have been obtained by Imbert. (...) Besides having noz component of their momentum, the energy-momentum quanta inside Fresnel's evanescent wave have typical tachyon properties, the imaginary character of theiry component (normal to the reflecting surface) entailing that (in units such thatc=1) theirx component islarger than the energy quanta. Imbert is now planning experiments to test these interesting properties. Thus, the two main aspects of noncollinearity of velocity and momentum of spinning particles would be displayed. (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)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

Starting from the formal expressions of the hydrodynamical (or “local”) quantities employed in the applications of Clifford algebras to quantum mechanics, we introduce—in terms of the ordinary tensorial language—a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, we also propose a new (nonrelativistic) velocity operator for a spin- ${\frac{1}{2}}$ particle. This operator appears as the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a (...) second part associated with the so-called Zitterbewegung, which is the spin “internal” motion observed in the center-of-mass frame (CMF). This spin component of the velocity operator is nonzero not only in the Pauli theoretical framework, i.e., in the presence of external electromagnetic fields with a nonconstant spin function, but also in the Schrödinger case, when the wavefunction is a spin eigenstate. Thus, one gets even in the latter case a decomposition of the velocity field for the Madelung fluid into two distinct parts, which constitutes the nonrelativistic analogue of the Gordon decomposition for the Dirac current. Explicit calculations are presented for the velocity field in the particular cases of the hydrogen atom, of a spherical well potential, and of an electron in a uniform magnetic field. We find, furthermore, that the Zitterbewegung motion involves a velocity field which is solenoidal, and that the local angular velocity is parallel to the spin vector. In the presence of a nonuniform spin vector (Pauli case) we have, besides the component of the local velocity normal to the spin (present even in the Schrödinger theory), also a component which is parallel to the curl of the spin vector. (shrink)

A common assumption in non-relativistic quantum mechanics is that self-adjoint operators mathematically represent properties of quantum systems. Focusing on spin, we argue that a natural view considers observables as determinable properties and their eigenvalues as their corresponding determinates. We provide a taxonomy of the different views that one can hold, once it is accepted that spin can be modelled with the determinable-determinate relation. In particular, we present the two main families of views, dubbed Spin Monism and Pluralism, and we show (...) that the current literature does not take a stance between the two. Then we put forward two arguments in favour of the former. Finally, we present a new account of Spin Monism, that is absent in current literature; such a view is worth discussing, or so we contend, because several compelling considerations support it, and it opens new ways of thinking about the ontology of quantum mechanics. (shrink)

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been (...) shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a (...) classical-particle version of the Higgs mechanism. (shrink)

The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behaviour under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not (...) occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature. (shrink)

Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in spin-z (...) (as opposed to polar angle) independent of proximity to endpoints? (3) Why does spin “lock” in the vertical directions? The difficulties associated with (1) are rooted, as is Bell’s theorem, in the time-asymmetric assumption that the present distribution over hidden variables is independent of future settings. We believe, a priori of any of the experiments of modern physics, that such a time-asymmetric assumption is dubious when probing the microscopic scale. As for (2) and (3), they are simultaneously resolved by abandoning the fundamental distinction drawn between spin and spatial angular momentum, and by appealing to very tiny (in both magnitude and spatial extent) but numerous patches of magnetic noise in the Stern-Gerlach’s field. (shrink)

The key assumption is that of Leinaas and Myrheim and of Berry and Robbins, here specialized to spin zero: for n particles, the argument of the wave function should be the unordered multiplet {r 1,r 2,...,r n }. I also make use of the requirement that wave functions in the domain of the Hamiltonian must be continuous functions of the spatial variables. The new proof presented here has advantages of simplicity and transparency in comparison with earlier work based on (...) the same two principles and it uses weaker assumptions, especially avoiding the use of rotations of the relative coordinate of identical particles. (shrink)

It is generally believed that the de Broglie-Bohm model does not admit a particle interpretation for massive relativistic spin-0 particles, on the basis that particle trajectories cannot be defined. We show this situation is due to the fact that in the standard representation of the Klein-Gordon equation the wavefunction systematically contains superpositions of particle and anti-particle contributions. We argue that by working in a Foldy-Wouthuysen type representation uncoupling the particle from the anti-particle evolutions, a positive conserved density for a (...) particle and associated density current can be defined. For the free Klein-Gordon equation the velocity field obtained from this current density appears to be well-behaved and sub-luminal in typical instances. As an illustration, Bohmian trajectories for a spin-0 boson distribution are computed numerically for free propagation in situations in which the standard velocity field would take arbitrarily high positive and negative values. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

The Wigner distribution has proven to be a useful tool in many quantum problems requiring a joint distribution of position and momentum. In the present paper we develop a joint distribution for spin components within the spirit of the Wigner distribution. This distribution provides an insight into the quantum theory of measurement. We also discuss how one may write joint distributions for two arbitrary noncommuting operators.

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)

Quantum distribution functions for spin-1/2 systems are derived for various characteristic functions corresponding to different operator orderings.

Classical spinning particles are interpreted in terms of an underlying geometric theory. They are described by trajectories on the Poincaré group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2, C)×U(1)×SU(2) gauge theory, unifying gravity and the pre-Higgs standard model. The relation to parametrized relativistic quantum theory is discussed.

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis – i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the wave function of the system, which is conditional on the realized location values of the (...) particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm’s version of the EPR experiment. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Spin is a fundamental and distinctive property of the electron, having far-reaching implications. Yet its purely formal treatment often blurs the physical content and meaning of the spin operator and associated observables. In this work we propose to advance in disclosing the meaning behind the formalism, by first recalling some basic facts about the one-particle spin operator. Consistently informed by and in line with the quantum formalism, we then proceed to analyse in detail the spin projection operator correlation function \=\left\langle (...) \left \left \right\rangle \) for the bipartite singlet state, and show it to be amenable to an unequivocal probabilistic reading. In particular, the calculation of \\) entails a partitioning of the probability space, which is dependent on the directions \.\) The derivation of the CHSH- or other Bell-type inequalities, on the other hand, does not consider such partitioning. This observation puts into question the applicability of Bell-type inequalities to the bipartite singlet spin state. (shrink)

The problem of a relativistic spin-1/2 particle scattering from a step potential is solved within the theoretical framework of relativistic dynamics. This treatment avoids the Klein paradox. An experiment for testing the theory is suggested.

We prove that the classical theory with a discrete time (chronon) is a particular case of a more general theory in which spinning particles are associated with generalized Lagrangians containing time-derivatives of any order (a theory that has been called “Non-Newtonian Mechanics”). As a consequence, we get, for instance, a classical kinematical derivation of Hamiltonian and spin vector for the mentioned chronon theory (e.g., in Caldirola et al.’s formulation). Namely, we show that the extension of classical mechanics obtained (...) by the introduction of an elementary time-interval does actually entail the arising of an intrinsic angular momentum; so that it may constitute a possible alternative to string theory in order to account for the internal degrees of freedom of the microsystems. (shrink)

For relativistic particles with spin 1/2, which are described by the Dirac equation, a semiclassical trace formula is introduced that incorporates expectation values of observables in eigenstates of the Dirac-Hamiltonian. Furthermore, the semiclassical limit of an average of expectation values is expressed in terms of a classical average of the corresponding classical observable.

The traditional standard quantum mechanics theory is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle”. A complete and straightforward solution of the spin–statistics problem is presented on the basis of the “conformal quantum geometrodynamics” theory. This theory provides a Weyl-gauge invariant formulation of the standard quantum mechanics and reproduces successfully all relevant quantum processes including the formulation of Dirac’s or Schrödinger’s equation, of Heisenberg’s uncertainty relations and of the nonlocal EPR correlations. When the (...) conformal quantum geometrodynamics is applied to a system made of many identical particles with spin, an additional constant property of all elementary particles enters naturally into play: the “intrinsic helicity”. This property, not considered in the Standard Quantum Mechanics, determines the correct spin–statistics connection observed in Nature. (shrink)

A small number of minor typographical issues arose during the proofing process. The corrections are posted here.

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman position path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question “what happens when spin path integrals are computed over products of (...) MUBs?” Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons. (shrink)

Spin-statistics transmutation is the phenomenon occurring when a “dressing” transformation introduced for physical reasons (e.g. gauge invariance) modifies the “bare” spin and statistics of particles or fields. Historically, it first appeared in Quantum Mechanics and in semiclassical approximation to Quantum Field Theory. After a brief historical introduction, we sketch how to describe such phenomenon in Quantum Field Theory beyond the semiclassical approximation, using a path-integral formulation of euclidean correlation functions, exemplifying with anyons, dyons and skyrmions.

We present a simple first step toward a relativistically covariant generalization of the Bohm-Bub hidden-variable theory. The model is applicable to spin measurement on a single Dirac particle and describes the collapse of the state vector to a spin-up or spin-down state. The essential postulate is that the hidden-variable vector transforms in the same way as the state vector under a Lorentz transformation. This yields a covariant collapse equation, which reduces to the ordinary Bohm-Bub equation for an observer stationary with (...) respect to the particle and shows a time dilated collapse for a moving observer. The model yields the correct quantum transition probabilities for all observers. (shrink)

We develop here the general treatment of the Bethe—Salpeter equation for the bound state of two spin-l particles interacting through an electromagnetic interaction. The treatment here, which can be generalized to strong interactions, combines the two-component approach utilized previously by the author in conjunction with spontaneous symmetry breaking. This is done by using a Lagrangian having SU(2)×U(1) symmetry (without fermions) and then choosing the ′t Hooft gauge. In this way, a renormalizable theory for the interaction of two spin-l (...) class='Hi'>particles via an electromagnetic interaction is ensured. (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)

In this paper I discuss how Bohm's interpretation models spin measurements and how the two ways in which spin is a contextual property pertains to the Kochen-Specker theorem. I then present locality principles from which a Bell Inequality can be derived, and I identify which of the locality principles Bohm's interpretation violates at which times. I also present reasons why the spin vector should not be attributed to the Bohmian particles.

The self-interaction spin-2 approach to GR has been extremely influential in the particle physics community. Leaving no doubt regarding its heuristic value, we argue that any view of the metric field of GR as nothing but a stand-in for a self-coupling field in at spacetime runs into a dilemma: either the view is physically incomplete in so far as it requires recourse to GR after all, or it leads to an absurd multiplication of alternative viewpoints on GR rendering any understanding (...) of the metric field as nothing but a spin-2 field in at spacetime unjustified. (shrink)

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue (...) that permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)

Several theoretical publications on the Dirac equation published during the last decades have shown that, an interpretation is possible, which ascribes the origin of electron spin and magnetic moment to an autonomous circular motion of the point-like charged particle around a fixed centre. In more recent publications an extension of the original so called “Zitterbewegung Interpretation” of quantum mechanics was suggested, in which the spin results from an average of instantaneous spin vectors over a Zitterbewegung period. We argue that, the (...) corresponding autonomous motion of the electron should, if it is real, determine non-relativistic spin measurements. Such a direct connection with the established formal quantum mechanical description of spin measurements, into which spin is introduced as a “non-classical” quantity has, to our knowledge, not been reported. In the present work we show that, under certain “model assumptions” concerning the proposed autonomous motion, results of spin measurements, including measurements of angular correlations in singlet systems, can indeed be correctly described using classical probabilities. The success of the model is evidence for the “reality” of the assumed autonomous motion. The resulting model violates the Bell—inequalities to the same extent as quantum mechanics. (shrink)

CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT (...) and Spin-Statistics theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View. I will argue that such proofs suggest the Received View’s approach to ontology is flawed. (shrink)

Medium- and high-spin states of Pr-134 were populated using the Cd-116(Na-23, 5n) reaction and studied with the GAMMASPHERE spectrometer. Several new bands have been found in this nucleus, one of them being linked to the previously observed chiral-candidate twin-band structure. The ground state of Pr-134 could be determined through establishing a level structure that connects the two previously known long-lived isomeric states. Unambiguous spin-parity assignments for the excited states could be performed based on the known 2(-) spin-parity of the ground (...) state combined with the present experimental data. Intrinsic single-particle configurations have been assigned to the newly observed bands on the basis of the measured B(M1)/B(E2) ratios, alignments, band-crossing frequencies, bandhead spins, the observed single-particle configurations in the neighboring nuclei, and taking into account the predictions of total Routhian surface and tilted-axis cranking calculations. (shrink)

The significance of the de Broglie/Bohm hidden-particle position in the relativistic regime is addressed, seeking connection to the single-particle Newton–Wigner position. The effect of non-positive excursions of the ensemble density for extreme cases of positive-energy waves is easily computed using an integral of the equations of motion developed here for free spin-0 particles in 1 + 1 dimensions and is interpreted in terms of virtual-like pair creation and annihilation beneath the Compton wavelength. A Bohm-theoretic description of the acausal explosion (...) of a specific Newton–Wigner-localized state is presented in detail. The presence of virtual pairs found is interpreted as the Bohm picture of the spatial extension beyond single point particles proposed in the 1960s as to why space-like hyperplane dependence of the Newton–Wigner wavefunctions may be needed to achieve Lorentz covariance. For spin-1/2 particles the convective current is speculatively utilized for achieving parity with the spin-0 theory. The spin-0 improper quantum potential is generalized to an improper stress tensor for spin-1/2 particles. (shrink)

The difficulties of relativistic particle theories formulated by means of canonical quantization, such as those of Klein–Gordon and Dirac, ultimately led theoretical physicists to turn to quantum field theory to model elementary particle physics. In order to overcome these difficulties, the theories of the present approach are developed deductively from the physical principles that specify the system, without making use of canonical quantization. For a free particle these starting assumptions are invariance of the theory and covariance of position with respect (...) to Poincaré transformations. In pursuing the approach, the effectiveness of group theoretical methods is exploited. The coherent development of our program has shown that robust classes of representations of the Poincaré group, discarded by the known particle theories, can in fact be taken as bases for perfectly consistent theories. For massive spin zero particles, six inequivalent theories have been determined, two of which do not correspond to any of the current ones; all of these theories overcome the difficulties of Klein–Gordon one. The present lack of the explicit transformation properties of position with respect to boosts prevents the complete determination of non zero spin particle theories. In the past a particular form of these transformation properties was adopted by Jordan and Mukunda. We check its consistency within the present approach and find that for spin \ particles there is only one consistent theory, which is unitarily related to Dirac’s; yet, once again, it requires classes of irreducible representations previously discarded. (shrink)

Leibniz’s _principium identitatis indiscernibilium _excludes the existence of two different objects possessing all properties identical. Although perfectly acceptable for macroscopic systems, it becomes questionable in quantum mechanics, where the concept of identical particles is quite natural and has measurable consequences. On the other hand, Leibniz’s principle seems to be indispensable when we want to individuate an item and ascribe to it particular property (e.g. value of the projection of spin on a chosen axis). We may thus abandon the principle (...) on the quantum level, claiming it falsity here, or (better) try to find other ways of individuation of objects, possibly by adopting appropriately the very concept of it. All these problems, and many other connected with identity and indiscernibility of quantum objects, are thoroughly discussed in the book of Tomasz Bigaj, unique in the world literature due to its comprehensiveness. (shrink)

The aim of this paper is to offer a conceptual analysis of Weinberg's proof of the spin-statistics theorem by comparing it with Pauli's original proof and with the subsequent textbook tradition, which typically resorts to the dichotomy positive energy for half-integral spin particles/microcausality for integral-spin particles. In contrast to this tradition, Weinberg's proof does not directly invoke the positivity of the energy, but derives the theorem from the single relativistic requirement of microcausality. This seemingly innocuous difference marks an (...) important change in the conceptual basis of quantum physics. Its historical, theoretical, and conceptual roots are here reconstructed. The link between Weinberg's proof and Pauli's original is highlighted: Weinberg's proof turns out to do justice to Pauli's anti-Dirac lines of thought. The work of Furry and Oppenheimer is also surveyed as a “third way” between the textbook tradition established by Pauli and Weinberg's approach. (shrink)

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom for stability, along (...) with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions imply that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed. (shrink)

A deterministic model that accounts for the statistical behavior of random samples of identical particles is presented. The model is based on some nonmeasurable distribution of spin values in all directions. The mathematical existence of such distributions is proved by set-theoretical techniques, and the relation between these distributions and observed frequencies is explored within an appropriate extension of probability theory. The relation between quantum mechanics and the model is specified. The model is shown to be consistent with known polarization (...) phenomena and the existence of macroscopic magnetism. Finally.. (shrink)

In this work we review the derivation of Dirac and Weinberg equations based on a “principle of indistinguishability” for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j≥1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields $\mathcal{O}(p^{2j} )$ equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG for (...) a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j= $ - \frac{1}{2}$ , there exists no Dirac-like equation for the (j,0)⊕(0,j) representation nor for the ( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ ) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)⊕( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ )⊕(0,1) representation by this method and show that the (1, $ - \frac{1}{2}$ )⊕( $ - \frac{1}{2}$ ,1) representation satisfies a Dirac-like equation which describes a multiplet of $j = \frac{3}{2}{\text{ and }}j = \frac{1}{2}$ with masses m and m/2, respectively. (shrink)

Quasi-probability distribution functions fj WW, fj MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fj sph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.

The parametrized Duffin–Kemmer–Petiau wave equation is formulated for many relativistic particles of spin-0 or spin-1. The first-quantized formulation lacks the fields of creation and annihilation operators which satisfy commutation relations subject to causality conditions, and which are essential to the Quantum Field Theoretic proof of the spin-statistics connection. It is instead proved that the wavefunctions for identical particles must be symmetric by extension of the nonrelativistic argument of Jabs. The causal commutators of Quantum Field Theory restrict entanglement to (...) separations of the order of the Compton wavelength \. The entanglement manifest in the symmetric Duffin–Kemmer–Petiau wavefunctions is unrestricted. (shrink)