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  1. Stephen L. Adler & Jeeva Anandan (1996). Nonadiabatic Geometric Phase in Quaternionic Hilbert Space. Foundations of Physics 26 (12):1579-1589.
    We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
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  2. Alexander Afriat (2013). Weyl's Gauge Argument. Foundations of Physics 43 (5):699-705.
    The standard $\mathbb{U}(1)$ “gauge principle” or “gauge argument” produces an exact potential A=dλ and a vanishing field F=d 2 λ=0. Weyl (in Z. Phys. 56:330–352, 1929; Rice Inst. Pam. 16:280–295, 1929) has his own gauge argument, which is sketchy, archaic and hard to follow; but at least it produces an inexact potential A and a nonvanishing field F=dA≠0. I attempt a reconstruction.
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  3. B. E. Allman, A. Cimmino, S. L. Griffin & A. G. Klein (1999). Quantum Phase Shift Caused by Spatial Confinement. Foundations of Physics 29 (3):325-332.
    This paper presents the results of optical interferometry experiments in which the phase of photons in one arm of a Mach-Zehnder interferometer is modified by applying a transverse constriction. An equivalent quantum interferometry experiment using neutron de Broglie waves is discussed in which the observed phase shift is in the spirit of the force-free phase shift of the Aharonov-Bohm effects. In the optical experiments the experimental results are in excellent agreement with predictions.
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  4. P. K. Anastasovski, T. E. Bearden, C. Ciubotariu, W. T. Coffey, L. B. Crowell, G. J. Evans, M. W. Evans, R. Flower, A. Labounsky, B. Lehnert, P. R. Molnár, S. Roy & J. P. Vigier (2000). Operator Derivation of the Gauge-Invariant Proca and Lehnert Equations; Elimination of the Lorenz Condition. Foundations of Physics 30 (7):1123-1129.
    Using covariant derivatives and the operator definitions of quantum mechanics, gauge invariant Proca and Lehnert equations are derived and the Lorenz condition is eliminated in U(1) invariant electrodynamics. It is shown that the structure of the gauge invariant Lehnert equation is the same in an O(3) invariant theory of electrodynamics.
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  5. F. Antonuccio, S. Pinsky & S. Tsujimaru (2000). A Comment on the Light-Cone Vacuum in 1+1 Dimensional Super-Yang–Mills Theory. Foundations of Physics 30 (3):475-486.
    The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious “zero-mode” problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the gauge (...)
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  6. David Atkinson, Running Coupling in Nonperturbative QCD: Bare Vertices and y-Max Approximation.
    A recent claim that in quantum chromodynamics in the Landau gauge the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson- Schwinger equations are taken to be bare. The gauge invariant running coupling is shown to be uniquely determined by the equations and to have a large finite infrared (...)
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  7. Jürgen Audretsch & Vladimir D. Skarzhinsky (1998). Quantum Processes Beyond the Aharonov-Bohm Effect. Foundations of Physics 28 (5):777-788.
    We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the (...)
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  8. Jonathan Bain (2008). Richard Healey:Gauging What's Real: The Conceptual Foundations of Contemporary Gauge Theories,:Gauging What's Real: The Conceptual Foundations of Contemporary Gauge Theories. Philosophy of Science 75 (4):479-485.
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  9. Rabin Banerjee, Biswajit Chakraborty, Subir Ghosh, Pradip Mukherjee & Saurav Samanta (2009). Topics in Noncommutative Geometry Inspired Physics. Foundations of Physics 39 (12):1297-1345.
    In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.
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  10. Julian Barbour (2010). The Definition of Mach's Principle. Foundations of Physics 40 (9-10):1263-1284.
    Two definitions of Mach’s principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity.
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  11. Robert Batterman (2003). Falling Cats, Parallel Parking, and Polarized Light. Studies in History and Philosophy of Science Part B 34 (4):527-557.
    This paper addresses issues surrounding the concept of geometric phase or "anholonomy". Certain physical phenomena apparently require for their explanation and understanding, reference to toplogocial/geometric features of some abstract space of parameters. These issues are related to the question of how gauge structures are to be interpreted and whether or not the debate over their "reality" is really going to be fruitful.
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  12. R. G. Beil (1995). Moving Frame Transport and Gauge Transformations. Foundations of Physics 25 (5):717-742.
    An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, (...)
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  13. Gordon Belot, An Elementary Notion of Gauge Equivalence.
    An elementary notion of gauge equivalence is introduced that does not require any Lagrangian or Hamiltonian apparatus. It is shown that in the special case of theories, such as general relativity, whose symmetries can be identified with spacetime diffeomorphisms this elementary notion has many of the same features as the usual notion. In particular, it performs well in the presence of asymptotic boundary conditions.
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  14. Gordon Belot (2001). The Principle of Sufficient Reason. Journal of Philosophy 98 (2):55-74.
    The paper is about the physical theories which result when one identifies points in phase space related by symmetries; with applications to problems concerning gauge freedom and the structure of spacetime in classical mechanics.
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  15. Gordon Belot (1998). Understanding Electromagnetism. British Journal for the Philosophy of Science 49 (4):531-555.
    It is often said that the Aharonov-Bohm effect shows that the vector potential enjoys more ontological significance than we previously realized. But how can a quantum-mechanical effect teach us something about the interpretation of Maxwell's theory—let alone about the ontological structure of the world—when both theories are false? I present a rational reconstruction of the interpretative repercussions of the Aharonov-Bohm effect, and suggest some morals for our conception of the interpretative enterprise.
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  16. Gordon Belot, John Earman, Richard Healey, Tim Maudlin, Antigone Nounou & Ward Struyve, Synopsis and Discussion: Philosophy of Gauge Theory.
    This document records the discussion between participants at the workshop "Philosophy of Gauge Theory," Center for Philosophy of Science, University of Pittsburgh, 18-19 April 2009.
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  17. R. Blanco (1999). On a Hypothetical Explanation of the Aharonov-Bohm Effect. Foundations of Physics 29 (5):693-720.
    I study in detail a proposal made by T. H. Boyer in an attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In this paper (...)
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  18. Timothy H. Boyer (2008). Comment on Experiments Related to the Aharonov–Bohm Phase Shift. Foundations of Physics 38 (6):498-505.
    Recent experiments undertaken by Caprez, Barwick, and Batelaan should clarify the connections between classical and quantum theories in connection with the Aharonov–Bohm phase shift. It is pointed out that resistive aspects for the solenoid current carriers play a role in the classical but not the quantum analysis for the phase shift. The observed absence of a classical lag effect for a macroscopic solenoid does not yet rule out the possibility of a lag explanation of the observed phase shift for a (...)
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  19. Timothy H. Boyer (2002). Classical Electromagnetic Interaction of a Point Charge and a Magnetic Moment: Considerations Related to the Aharonov–Bohm Phase Shift. Foundations of Physics 32 (1):1-39.
    A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a connection between (...)
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  20. Timothy H. Boyer (2002). Semiclassical Explanation of the Matteucci–Pozzi and Aharonov–Bohm Phase Shifts. Foundations of Physics 32 (1):41-49.
    Classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric dipoles or a line of magnetic dipoles (a solenoid) is placed between the electron beams forming the interference pattern.
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  21. Timothy H. Boyer (2000). Classical Electromagnetism and the Aharonov–Bohm Phase Shift. Foundations of Physics 30 (6):907-932.
    Although there is good experimental evidence for the Aharonov–Bohm phase shift occurring when a solenoid is placed between the beams forming a double-slit electron interference pattern, there has been very little analysis of the relevant classical electromagnetic forces. These forces between a point charge and a solenoid involve subtle relativistic effects of order v 2 /c 2 analogous to those discussed by Coleman and Van Vleck in their treatment of the Shockley–James paradox. In this article we show that a treatment (...)
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  22. Timothy H. Boyer (2000). Does the Aharonov–Bohm Effect Exist? Foundations of Physics 30 (6):893-905.
    We draw a distinction between the Aharonov–Bohm phase shift and the Aharonov–Bohm effect. Although the Aharonov–Bohm phase shift occurring when an electron beam passes around a magnetic solenoid is well-verified experimentally, it is not clear whether this phase shift occurs because of classical forces or because of a topological effect occurring in the absence of classical forces as claimed by Aharonov and Bohm. The mathematics of the Schroedinger equation itself does not reveal the physical basis for the effect. However, the (...)
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  23. Katherine A. Brading & Elena Castellani (eds.) (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press.
    Highlighting main issues and controversies, this book brings together current philosophical discussions of symmetry in physics to provide an introduction to the subject for physicists and philosophers. The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, (...)
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  24. Katherine Brading & Harvey R. Brown (2004). Are Gauge Symmetry Transformations Observable? British Journal for the Philosophy of Science 55 (4):645-665.
    In a recent paper in the British Journal for the Philosophy of Science, Kosso discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by ’t Hooft has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper we present our preferred approach to the empirical (...)
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  25. Paul Busch (1990). On the Energy-Time Uncertainty Relation. Part II: Pragmatic Time Versus Energy Indeterminacy. [REVIEW] Foundations of Physics 20 (1):33-43.
    The discussion of a particular kind of interpretation of the energy-time uncertainty relation, the “pragmatic time” version of the ETUR outlined in Part I of this work [measurement duration (pragmatic time) versus uncertainty of energy disturbance or measurement inaccuracy] is reviewed. Then the Aharonov-Bohm counter-example is reformulated within the modern quantum theory of unsharp measurements and thereby confirmed in a rigorous way.
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  26. Adam Caprez & Herman Batelaan (2009). Feynman's Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect. Foundations of Physics 39 (3):295-306.
    An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.
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  27. M. Carmeli & S. Malin (1987). Field Theory onR×S 3 Topology. V:SU 2 Gauge Theory. [REVIEW] Foundations of Physics 17 (2):193-200.
    A gauge theory on R×S 3 topology is developed. It is a generalization to the previously obtained field theory on R×S 3 topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences (...)
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  28. Elena Castellani, Dirac on Gauges and Constraints.
    This paper is devoted to examining the relevance of Dirac's view on the use of transformation theory and invariants in modern physics --- as it emerges from his 1930 book on quantum mechanics as well as from his later work on singular theories and constraints --- to current reflections on the meaning of physical symmetries, especially gauge symmetries.
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  29. Gabriel López Castro & Alejandro Mariano (2003). Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters. Foundations of Physics 33 (5):719-734.
    The elastic and radiative π + p scattering are studied in the framework of an effective Lagrangian model for the Δ ++ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole (Δ ++) and background contributions (ρ 0, σ, Δ, and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters (...)
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  30. J. S. R. Chisholm & R. S. Farwell (1995). Unified Spin Gauge Model and the Top Quark Mass. Foundations of Physics 25 (10):1511-1522.
    Spin gauge models use a real Clifford algebraic structure Rp,q associated with a real manifold of dimension p + q to describe the fundamental interactions of elementary particles. This review provides a comparison between those models and the standard model, indicating their similarities and differences. By contrast with the standard model, the spin gauge model based on R3,8 generates intermediate boson mass terms without the need to use the Higgs-Kibble mechanism and produces a precise prediction for the mass of the (...)
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  31. R. Eugene Collins (1996). Differentiable Probabilities: A New Viewpoint on Spin, Gauge Invariance, Gauge Fields, and Relativistic Quantum Mechanics. [REVIEW] Foundations of Physics 26 (11):1469-1527.
    A new approach to developing formulisms of physics based solely on laws of mathematics is presented. From simple, classical statistical definitions for the observed space-time position and proper velocity of a particle having a discrete spectrum of internal states we derive u generalized Schrödinger equation on the space-time manifold. This governs the evolution of an N component wave function with each component square integrable over this manifold and is structured like that for a charged particle in an electromagnetic field but (...)
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  32. N. C. A. Da Costa, F. A. Doria, A. F. Furtado-do-Amaral & J. A. De Barros (1994). Two Questions on the Geometry of Gauge Fields. Foundations of Physics 24 (5):783-800.
    We first show that a theorem by Cartan that generalizes the Frobenius integrability theorem allows us (given certain conditions) to obtain noncurvature solutions for the differential Bianchi conditions and for higher-degree similar relations. We then prove that there is no algorithmic procedure to determine, for a reasonable restricted algebra of functions on spacetime, whether a given connection form satisfies the preceding conditions. A parallel result gives a version of Gödel's first incompleteness theorem within an (axiomatized) theory of gauge fields.
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  33. C. Dariescu & Marina Dariescu (1991). U(1) Gauge Theory of the Quantum Hall Effect. Foundations of Physics 21 (11):1329-1333.
    The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.
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  34. C. Dariescu & Marina Dariescu (1991). U(1) Gauge Theory for Charged Bosonic Fields onR×S 3 Topology. Foundations of Physics 21 (11):1323-1327.
    A model for U(1) gauge theories over a compact Lie group is described usingR×S 3 as background space. A comparison with other results is given. Electrodynamics equations are obtained. Finally, some considerations and observations about gravity onR×S 3 space are presented.
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  35. Ciprian Dariescu & Marina-Aura Dariescu (1994). SU (2)× U (1) Gauge Theory of Bosonic and Fermionic Fields inS 3× R Space-Time. Foundations of Physics 24 (11):1577-1582.
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  36. Marina -Aura Dariescu, C. Dariescu & I. Gottlieb (1995). Gauge Theory of Fermions onR × S 3 Spacetime. Foundations of Physics 25 (6):959-963.
    A Lorentz-invariant gauge theory for massive fermions on R × S 3 spacetime is built up. Using the symmetry of S 3,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S 3 spacetime, pointing out major differences from the Minkowskian case.
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  37. Marina-Aura Dariescu, C. Dariescu & I. Gottlieb (1995). Gauge Theory of Fermions onR× S 3 Spacetime. Foundations of Physics 25 (6):959-963.
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  38. O. Costa de Beauregard (2004). To Believe Or Not Believe In The A Potential, That's a Question. Flux Quantization in Autistic Magnets. Prediction of a New Effect. 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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  39. O. Costa de Beauregard (1992). Electromagnetic Gauge as an Integration Condition: De Broglie's Argument Revisited and Expanded. [REVIEW] Foundations of Physics 22 (12):1485-1494.
    Einstein's mass-energy equivalence law, argues de Broglie, by fixing the zero of the potential energy of a system,ipso facto selects a gauge in electromagnetism. We examine how this works in electrostatics and in magnetostatics and bring in, as a “trump card,” the familiar, but highly peculiar, system consisting of a toroidal magnet m and a current coil c, where none of the mutual energy W resides in the vacuum. We propose the principle of a crucial test for measuring the fractions (...)
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  40. J. A. De Wet (1987). Nuclear Structure on a Grassmann Manifold. Foundations of Physics 17 (10):993-1018.
    Products of particlelike representations of the homogeneous Lorentz group are used to construct the degrees of spin angular momentum of a composite system of protons and neutrons. If a canonical labeling system is adopted for each state, a shell structure emerges. Furthermore the use of the Dirac ring ensures that the spin is characterized by half-angles in accord with the neutron-rotation experiment. It is possible to construct a Clebsch-Gordan decomposition to reduce a state of complex angular momentum into simpler states (...)
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  41. Francisco Antonio Doria (2009). Theoretical Physics: A Primer for Philosophers of Science. Principia 13 (2):195-232.
    We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.
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  42. W. Drechsler (1992). Quantized Fiber Dynamics for Extended Elementary Objects Involving Gravitation. Foundations of Physics 22 (8):1041-1077.
    The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to (...)
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  43. W. Drechsler (1989). Modified Weyl Theory and Extended Elementary Objects. Foundations of Physics 19 (12):1479-1497.
    To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the domains (...)
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  44. Wolfgang Drechsler & Eduard Prugovečki (1991). Geometro-Stochastic Quantization of a Theory for Extended Elementary Objects. 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 $_{\bar (...)
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  45. I. H. Duru (1993). Casimir Force Between Two Aharonov-Bohm Solenoids. Foundations of Physics 23 (5):809-818.
    The vacuum structure for the massive charged scalar field in the region of two parallel, infinitely long and thin solenoids confining the fluxesn 1 andn 2 is studied. By using the Green function method, it is found that the vacuum expectation value of the system's energy has a finite mutual interaction term depending on the distance a between the solenoids, which implies an attractive force per unit length given by F n1n2 =−(ℏc/π2)(n 1 n 2)2/a 3.
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  46. John Earman (2002). Gauge Matters. Proceedings of the Philosophy of Science Association 2002 (3):S209--20.
    The constrained Hamiltonian formalism is recommended as a means for getting a grip on the concepts of gauge and gauge transformation. This formalism makes it clear how the gauge concept is relevant to understanding Newtonian and classical relativistic theories as well as the theories of elementary particle physics; it provides an explication of the vague notions of "local" and "global" gauge transformations; it explains how and why a fibre bundle structure emerges for theories which do not wear their bundle structure (...)
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  47. M. W. Evans (1995). The Charge Quantization Condition inO(3) Vacuum Electrodynamics. 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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  48. Tim Oliver Eynck, Holger Lyre & Nicolai von Rummell, A Versus B! Topological Nonseparability and the Aharonov-Bohm Effect.
    Since its discovery in 1959 the Aharonov-Bohm effect has continuously been the cause for controversial discussions of various topics in modern physics, e.g. the reality of gauge potentials, topological effects and nonlocalities. In the present paper we juxtapose the two rival interpretations of the Aharonov-Bohm effect. We show that the conception of nonlocality encountered in the Aharonov-Bohm effect is closely related to the nonseparability which is common in quantum mechanics albeit distinct from it due to its topological nature. We propose (...)
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  49. T. E. Feuchtwang, E. Kazes & P. H. Cutler (1986). Generalized Gauge Independence and the Physical Limitations on the von Neumann Measurement Postulate. Foundations of Physics 16 (12):1263-1284.
    An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical (...)
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  50. D. Fine & A. Fine (1997). Gauge Theory, Anomalies and Global Geometry: The Interplay of Physics and Mathematics. Studies in History and Philosophy of Science Part B 28 (3):307-323.
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