Results for 'Quantization'

265 found
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  1.  36
    Unambiguous Quantization From the Maximum Classical Correspondence That Is Self-Consistent: The Slightly Stronger Canonical Commutation Rule Dirac Missed. [REVIEW]Steven Kenneth Kauffmann - 2011 - Foundations of Physics 41 (5):805-819.
    Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac’s canonical commutation rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson (...)
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  2.  58
    Rarita-Schwinger Quantum Free Field Via Deformation Quantization.B. Carballo Pérez & H. García-Compeán - 2012 - Foundations of Physics 42 (3):362-368.
    Rarita-Schwinger (RS) quantum free field is reexamined in the context of deformation quantization (DQ). It is interesting to consider this alternative for the specific case of the spin 3/2 field because DQ avoids the problem of dealing from the beginning with the extra degrees of freedom which appears in the conventional canonical quantization. It is found out that the subsidiary condition does not introduce any change either in the Wigner function or in other aspects of the Weyl-Wigner-Groenewold-Moyal formalism, (...)
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  3.  53
    BRST Extension of Geometric Quantization.Ronald Fulp - 2007 - Foundations of Physics 37 (1):103-124.
    Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the physics (...)
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  4.  38
    Energy for Two-Electron Quantum Dots: The Quantization Rule Approach. [REVIEW]Xiao-Yan Gu - 2006 - Foundations of Physics 36 (12):1884-1892.
    The energy spectra for two electrons in a parabolic quantum dot are calculated by the quantization rule approach. The numerical results are in excellent agreement with the results by the method of integrating directly the Schrödinger equation, and better than those by the WKB method and the WKB-DP method.
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  5.  36
    The Wave Function Collapse as an Effect of Field Quantization.K. Lewin - 2009 - Foundations of Physics 39 (10):1145-1160.
    It is pointed out that ordinary quantum mechanics as a classical field theory cannot account for the wave function collapse if it is not seen within the framework of field quantization. That is needed to understand the particle structure of matter during wave function evolution and to explain the collapse as symmetry breakdown by detection. The decay of a two-particle bound s state and the Stern-Gerlach experiment serve as examples. The absence of the nonlocality problem in Bohm’s version of (...)
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  6.  34
    Canonical Quantization of a Massive Weyl Field.Maxim Dvornikov - 2012 - Foundations of Physics 42 (11):1469-1479.
    We construct a consistent theory of a quantum massive Weyl field. We start with the formulation of the classical field theory approach for the description of massive Weyl fields. It is demonstrated that the standard Lagrange formalism cannot be applied for the studies of massive first-quantized Weyl spinors. Nevertheless we show that the classical field theory description of massive Weyl fields can be implemented in frames of the Hamilton formalism or using the extended Lagrange formalism. Then we carry out a (...)
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  7.  27
    Topological Quantization of the Magnetic Flux.Antonio F. Rañada & José Luis Trueba - 2006 - Foundations of Physics 36 (3):427-436.
    The quantization of the magnetic flux in superconducting rings is studied in the frame of a topological model of electromagnetism that gives a topological formulation of electric charge quantization. It turns out that the model also embodies a topological mechanism for the quantization of the magnetic flux with the same relation between the fundamental units of magnetic charge and flux as there is between the Dirac monopole and the fluxoid.
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  8.  22
    Born–Jordan Quantization and the Equivalence of the Schrödinger and Heisenberg Pictures.Maurice A. de Gosson - 2014 - Foundations of Physics 44 (10):1096-1106.
    The aim of the famous Born and Jordan 1925 paper was to put Heisenberg’s matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg’s theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger’s wave mechanics cannot be equivalent to Heisenberg’s more physically motivated matrix mechanics unless its observables are quantized using this rule, and not (...)
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  9.  22
    The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization.Nikolai N. Bogolubov & Anatoliy K. Prykarpatsky - 2010 - Foundations of Physics 40 (5):469-493.
    The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations (...)
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  10.  51
    Optimization and Quantization in Gradient Symbol Systems: A Framework for Integrating the Continuous and the Discrete in Cognition.Paul Smolensky, Matthew Goldrick & Donald Mathis - 2014 - Cognitive Science 38 (6):1102-1138.
    Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, (...)
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  11. Quantization as a Guide to Ontic Structure.Karim P. Y. Thébault - 2016 - British Journal for the Philosophy of Science 67 (1):89-114.
    The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilizing the formal procedure of quantization as a guide to ontic structure of modern physical theory. The example (...)
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  12.  14
    Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-Model Reduction.Joshua Rosaler - 2018 - Foundations of Physics 48 (3):355-385.
    This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum–classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \, and, on the other, a certain generalization of Ehrenfest’s Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation (...)
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  13.  19
    Action Quantization, Energy Quantization, and Time Parametrization.Edward R. Floyd - 2017 - Foundations of Physics 47 (3):392-429.
    The additional information within a Hamilton–Jacobi representation of quantum mechanics is extra, in general, to the Schrödinger representation. This additional information specifies the microstate of \ that is incorporated into the quantum reduced action, W. Non-physical solutions of the quantum stationary Hamilton–Jacobi equation for energies that are not Hamiltonian eigenvalues are examined to establish Lipschitz continuity of the quantum reduced action and conjugate momentum. Milne quantization renders the eigenvalue J. Eigenvalues J and E mutually imply each other. Jacobi’s theorem (...)
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  14.  79
    Second Quantization of the Stueckelberg Relativistic Quantum Theory and Associated Gauge Fields.L. P. Horwitz & N. Shnerb - 1998 - Foundations of Physics 28 (10):1509-1519.
    The gauge compensation fields induced by the differential operators of the Stueckelberg-Schrödinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields; An action is constructed and the second quantization of the fields carried out using a constraint procedure. The properties of the second quantized matter fields are discussed.
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  15. A Classical Explanation of Quantization.Gerhard Grössing, Johannes Mesa Pascasio & Herbert Schwabl - 2011 - Foundations of Physics 41 (9):1437-1453.
    In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of purely classical physics. Moreover, under the same premises, also the energy spectrum of the quantum mechanical harmonic oscillator is derived. Essentially, Planck’s constant h is shown to be indicative of a particle’s “zitterbewegung” and thus of a fundamental angular momentum. The latter is identified with (...)
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  16.  4
    Deformation quantization as an appropriate guide to ontic structure.Aboutorab Yaghmaie - forthcoming - Synthese:1-23.
    Karim Thébault has argued that for ontic structural realism to be a viable ontology it should accommodate two principles: physico-mathematical structures it deploys must be firstly consistent and secondly substantial. He then contends that in geometric quantization, a transitional machinery from classical to quantum mechanics, the two principles are followed, showing that it is a guide to ontic structure. In this article, I will argue that geometric quantization violates the consistency principle. To compensate for this shortcoming, the deformation (...)
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  17.  81
    A Relativistic Schrödinger-Like Equation for a Photon and Its Second Quantization.Donald H. Kobe - 1999 - Foundations of Physics 29 (8):1203-1231.
    Maxwell's equations are formulated as a relativistic “Schrödinger-like equation” for a single photon of a given helicity. The probability density of the photon satisfies an equation of continuity. The energy eigenvalue problem gives both positive and negative energies. The Feynman concept of antiparticles is applied here to show that the negative-energy states going backward in time (t → −t) give antiphoton states, which are photon states with the opposite helicity. For a given mode, properties of a photon, such as energy, (...)
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  18.  98
    Quantization by Parts, Self-Adjoint Extensions, and a Novel Derivation of the Josephson Equation in Superconductivity.K. Kong Wan & R. H. Fountain - 1996 - Foundations of Physics 26 (9):1165-1199.
    There has been a lot of interest in generalizing orthodox quantum mechanics to include POV measures as observables, namely as unsharp obserrables. Such POV measures are related to symmetric operators. We have argued recently that only maximal symmetric operators should describe observables.1 This generalization to maximal symmetric operators has many physical applications. One application is in the area of quantization. We shall discuss a scheme, to he called quantization by parts,which can systematically deal with what may be called (...)
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  19.  93
    A Path From the Quantization of the Action Variable to Quantum Mechanical Formalism.V. Hushwater - 1998 - Foundations of Physics 28 (2):167-184.
    Starting from the quantization of the action variable as a basic principle, I show that this leads one to the probabilistic description of physical quantities as random variables, which satisfy the uncertainty relation. Using such variables I show that the ensemble-averaged action variable in the quantum domain can be presented as a contour integral of a “quantum momentum function,” pq(z), which is assumed to be analytic. The condition that all bound states pq(z) must yield the quantized values of the (...)
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  20.  10
    Geometro-Stochastic Quantization of a Theory for Extended Elementary Objects.Wolfgang Drechsler & Eduard Prugovečki - 1991 - Foundations of Physics 21 (5):513-546.
    The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ (...)
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  21. Conceptual and Foundational Issues in the Quantization of Gravity.Steven Weinstein - 1998 - Dissertation, Northwestern University
    The quantization of gravity represents an important attempt at reconciling the two seemingly incompatible frameworks that lie at the base of modern physics, quantum theory and general relativity. The dissertation begins by looking at the incompatibilities between the two frameworks. The incompatibility with quantum theory, it is argued, is rooted in the profound differences between general relativity and ordinary field theories. The dissertation goes on to look at how, in practice, these incongruities are treated in the canonical quantization (...)
     
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  22.  75
    Quantic Fibers for Classical Systems: An Introduction to Geometric Quantization.Gabriel Catren - 2013 - Scientiae Studia 11 (1):35-74.
    En este artículo, se introducirá el formalismo de cuantificación canónica denominado "cuantificación geométrica". Dado que dicho formalismo permite entender la mecánica cuántica como una extensión geométrica de la mecánica clásica, se identificarán las insuficiencias de esta última resueltas por dicha extensión. Se mostrará luego como la cuantificación geométrica permite explicar algunos de los rasgos distintivos de la mecánica cuántica, como, por ejemplo, la noconmutatividad de los operadores cuánticos y el carácter discreto de los espectros de ciertos operadores. In this article, (...)
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  23.  33
    Quantization of Space-Time and the Corresponding Quantum Mechanics.M. Banai - 1985 - Foundations of Physics 15 (12):1203-1245.
    An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a “canonical” quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation [t,r]=±i $h =$ . The two cases will be considered simultaneously. In that case the event space is (...)
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  24.  66
    The Charge Quantization Condition inO(3) Vacuum Electrodynamics.M. W. Evans - 1995 - Foundations of Physics 25 (1):175-181.
    The existence of the longitudinal field B (3) in the vacuum implies that the gauge group of electrodynamics is O(3),and not U(1) [or O(2)].This results directly in the charge quantization condition e=h(ϰ/A (0)).This condition is derived independently in this paper from the relativistic motion of one electron in the field and is shown to he that in which the electron travels infinitesimally close to the speed of light.
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  25.  17
    On High Frequency Background Quantization of Gravity.H.-H. V. Borzeszkowski - 1982 - Foundations of Physics 12 (6):633-643.
    Considering background quantization of gravitational fields, it is generally assumed that the classical background satisfies Einstein's gravitational equations. However, there exist arguments showing that, for high frequency (quantum) fluctuations, this assumption has to be replaced by a condition describing the back reaction of fluctuations on the background. It is shown that such an approach leads to limitations for the quantum procedure which occur at distances larger than Planck's elementary lengthl=(Gh/c 3)1/2.
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  26.  58
    Classical Limit of Real Dirac Theory: Quantization of Relativistic Central Field Orbits. [REVIEW]Heinz Krüger - 1993 - Foundations of Physics 23 (9):1265-1288.
    The classical limit of real Dirac theory is derived as the lowest-order contribution in $\mathchar'26\mkern-10mu\lambda = \hslash /mc$ of a new, exact polar decomposition. The resulting classical spinor equation is completely integrated for stationary solutions to arbitrary central fields. Imposing single-valuedness on the covering space of a bivector-valued extension to these classical solutions, orbital angular momentum, energy, and spin directions are quantized. The quantization of energy turns out to yield the WKB formula of Bessey, Uhlenbeck, and Good. It is (...)
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  27.  48
    Periodic Orbit Quantization: How to Make Semiclassical Trace Formulae Convergent.Jörg Main & Günter Wunner - 2001 - Foundations of Physics 31 (3):447-474.
    Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of semiclassical recurrence functions. A band-limited periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. The frequencies of the periodic orbit signal are the semiclassical eigenvalues, and are determined by either linear predictor, Padé approximant, or signal diagonalization. The second method is based upon the (...)
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  28.  47
    Is There a Quantization Condition for the Classical Problem of Charge and Pole?H. A. Cohen - 1974 - Foundations of Physics 4 (1):115-120.
    In elementary derivations of the quantization of azimuthal angular momentum the eigenfunction is determined to be exp(im φ), which is “oversensitive” to the rotation φ → φ+2π, unlessm is an integer. In a recent paper Kerner examined the classical system of charge and magnetic pole, and expressed Π, a vector constant of motion for the system, in terms of a physical angle ψ, to deduce a remarkable paradox. Kerner pointed out that Π(ψ) is “oversensitive” to ψ → ψ+2π unless (...)
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  29.  1
    Paul Ehrenfest on the Necessity of Quanta : Discontinuity, Quantization, Corpuscularity, and Adiabatic Invariance.Enric Pérez & Luis Navarro - 2004 - Archive for History of Exact Sciences 58 (2):97-141.
    Our object in this paper is to study the antecedents, contents, implications, and impact of a not well-known or appreciated paper by EHRENFEST in 1911 on the essential nature of the different quantum hypotheses in radiation theory. After a careful analysis of EHRENFEST’s notebooks, correspondence, and publications, we conclude that the essential points of EHRENFEST’s paper were not perceived to a large extent, and hence that its implications were not considered thoroughly. Specifically, we show that EHRENFEST contributed significantly to the (...)
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  30.  44
    Quantum Probability and Unified Approach to Quantization and Dynamics.Blagowest A. Nikolov - 1996 - Foundations of Physics 26 (2):257-269.
    A simplified derivation of the Gudder-Hemion quantum probability formula is proposed. Defining configurations as the classical (q, p) deterministic states and generalized action as the (quantum) generating function of a canonical transformation, we obtain the usual quantization rules (for arbitrary polynomial quantities) and derive the Schrödinger wave equation on the same grounds. This approach suggests a statistical interpretation of the wave function in terms of the classical canonical transformations.
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  31.  43
    Geometric Quantization of the Five-Dimensional Kepler Problem.Ivailo M. Mladenov - 1991 - Foundations of Physics 21 (8):871-888.
    An extension of the Hurwitz transformation to a canonical transformation between phase spaces allows conversion of the five-dimensional Kepler problem into that of a constrained harmonic oscillator problem in eight dimensions. Thus a new regularization of the Kepler problem is established. Then, following Dirac, we quantize the extended phase space, imposing constraint conditions as superselection rules. In that way the interchangeability of the reduction and the quantization procedures is proved.
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  32.  41
    Canonical Quantization Without Conjugate Momenta.K. Just & L. S. The - 1986 - Foundations of Physics 16 (11):1127-1141.
    In the traditional form of canonical quantization, certain field components (not having “conjugate” momenta) must be regarded as noncanonical. This long-known distinction enters modern gauge theories, when they are canonically quantized as by Kugo and Ojima. We avoid that peculiarity by not using any conjugate “momenta” at all. In our formulation, canonical quantization can be related to Feynman's path integral.
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  33.  12
    Understanding Quantization.John R. Klauder - 1997 - Foundations of Physics 27 (11):1467-1483.
    The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a phase-space path integral, and at the same time establishes a fully satisfactory, geometric procedure of quantization.
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  34.  23
    Generalized Schrödinger Quantization.Robert Warren Finkel - 1973 - Foundations of Physics 3 (1):101-108.
    Schrödinger's original quantization procedure is extended to include observables with classical counterparts described in generalized coordinates and momenta. The procedure satisfies the superposition principle, the correspondence principle, Hermiticity requirements, and gauge invariance. Examples are given to demonstrate the derivation of operators in generalized coordinates or momenta. It is shown that separation of variables can be achieved before quantization.
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  35.  33
    Quantization in the Large.Daniel M. Greenberger - 1983 - Foundations of Physics 13 (9):903-951.
    A model theory is constructed that exhibits quantization on a cosmic scale. A holistic rationale for the theory is discussed. The theory incorporates a fundamental length, of cosmic size, and preserves the weak, geometrical equivalence principle. The momentum operator is an integral, nonlocal, naturally contravariant operator, in contrast to the usual quantum case. In the limit of high quantum numbers the theory reduces to classical physics, giving rise to a world which is quantized both on the microscopic and cosmic (...)
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  36.  18
    The Angular Momentum Dilemma and Born–Jordan Quantization.Maurice A. de Gosson - 2017 - Foundations of Physics 47 (1):61-70.
    The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated (...)
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  37.  28
    Path Integral Quantization of a Spinning Particle.Nuri Ünal - 1998 - Foundations of Physics 28 (5):755-762.
    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.
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  38.  6
    Combining Multiseismic Attributes with an Extended Octree Quantization Method.Saleh Al-Dossary, Jinsong Wang & Yuchun E. Wang - 2019 - Interpretation 7 (2):SC11-SC19.
    Seismic interpreters and processors encounter ever-increasing volumes of seismic attributes in geophysical exploration each year. Multiattribute integration and classification improve the ability to identify geologic facies and reservoir properties, such as thickness, fluid type, fracture intensity, and orientation. Simple color mixing technology allows us to display three attributes simultaneously. To overcome this limit, we extend from three nodes to up to eight nodes octree color quantization originated from image processing of compressing colors to handle eight groups of attributes to (...)
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  39.  24
    Hamiltonian Description and Quantization of Dissipative Systems.Charles P. Enz - 1994 - Foundations of Physics 24 (9):1281-1292.
    Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.
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  40.  20
    Topological Charge Quantization Via Path Integration: An Application of the Kustaanheimo-Stiefel Transformation. [REVIEW]Akira Inomata, Georg Junker & Raj Wilson - 1993 - Foundations of Physics 23 (8):1073-1091.
    The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bohm problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case. “Everything that is made beautiful and fair and lovely (...)
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  41.  13
    Canonical Quantization of a Nonrelativistic Singular Quasilinear System.T. Kawai - 1977 - Foundations of Physics 7 (3-4):185-204.
    Following Dirac's generalized canonical formalism, we develop a quantization scheme for theN-dimensional system described by the Lagrangian $L_0 (\dot y,y) = \frac{1}{2}h_{ij} (y)\dot y^i \dot y^j + b_i (y)\dot y^i - w(y)$ which is supposed to be invariant under the gauge transformation $y^i \to y\prime ^i = y^i + (\rho ^i _\alpha + \sigma ^i _{\alpha j} \dot y^j )\delta \Lambda ^\alpha + \tau ^i _\alpha \delta \dot \Lambda ^\alpha$ . The gauge invariance necessarily implies that the Lagrangian is (...)
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  42.  12
    The Quantization of the Hamiltonian in Curved Space.J. M. Domingos & M. H. Caldeira - 1984 - Foundations of Physics 14 (7):607-623.
    The construction of the quantum-mechanical Hamiltonian by canonical quantization is examined. The results are used to enlighten examples taken from slow nuclear collective motion. Hamiltonians, obtained by a thoroughly quantal method (generator-coordinate method) and by the canonical quantization of the semiclassical Hamiltonian, are compared. The resulting simplicity in the physics of a system constrained to lie in a curved space by the introduction of local Riemannian coordinates is emphasized. In conclusion, a parallel is established between the result for (...)
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  43.  10
    Electrodynamics in Terms of Functions Over the groupSU(2): II. Quantization[REVIEW]A. O. Barut, S. Malin & M. Semon - 1982 - Foundations of Physics 12 (5):521-530.
    In a previous article by two of the present authors Carmeli's group-theoretic method for the formulation of wave equations was applied to the case of the electromagnetic field, and the equations for the vector potential were derived. In the present paper a quantization procedure for these equations is carried out in the Lorentz gauge. It involves two independent variables, corresponding to the number of degrees of freedom of the electromagnetic field in a Hilbert space with a positive-definite metric. Conserved (...)
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  44.  25
    On the Choice of Algebra for Quantization.Benjamin H. Feintzeig - 2018 - Philosophy of Science 85 (1):102-125.
    In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.
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  45. Chaos, Quantization, and the Correspondence Principle.Robert W. Batterman - 1991 - Synthese 89 (2):189 - 227.
  46. The Problem of Time in Canonical Quantization of Relativistic Systems.Karel Kuchar - 1991 - In A. Ashtekar & J. Stachel (eds.), Conceptual Problems of Quantum Gravity. Birkhauser. pp. 141.
     
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  47.  62
    From Time Atoms to Space-Time Quantization: The Idea of Discrete Time, Ca 1925–1936.Helge Kragh & Bruno Carazza - 1994 - Studies in History and Philosophy of Science Part A 25 (3):437-462.
  48.  34
    Quantization in Generalized Coordinates.Gary R. Gruber - 1971 - Foundations of Physics 1 (3):227-234.
    The operator form of the generalized canonical momenta in quantum mechanics is derived by a new, instructive method and the uniqueness of the operator form is proven. If one wishes to find the correct representation of the generalized momentum operator, he finds the Hermitian part of the operator —iħ ∂/∂q, whereq q is the generalized coordinate. There are interesting philosophical implications involved in this: It is like saying that a physical structure is composed of two parts, one which is real (...)
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  49.  12
    Canonical Groups and the Quantization of Geometry and Topology.C. J. Isham - 1991 - In A. Ashtekar & J. Stachel (eds.), Conceptual Problems of Quantum Gravity. Birkhauser. pp. 358.
  50.  96
    To Believe Or Not Believe In The A Potential, That’s a Question. Flux Quantization in Autistic Magnets. Prediction of a New Effect.O. Costa de Beauregard - 2004 - Foundations of Physics 34 (11):1695-1702.
    Electromagnetic gauge as an integration condition was my wording in previous publications. I argue here, on the examples of the Möllenstaedt-Bayh and Tonomura tests of the Ahraronov–Bohm (AB) effect, that not only the trapped flux Φ but also, under the integration condition A ≡ 0 if Φ = 0, the local value of the vector potential is measured.
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