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  1. M. C. B. Abdalla (1988). Analytic Stochastic Regularization: Gauge and Supersymmetric Theories. Scientia 52:273.
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  2. 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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  3. Alexander Afriat, Is the World Made of Loops?
    In discussions of the Aharonov-Bohm effect, Healey and Lyre have attributed reality to loops $\sigma_0$ (or hoops $[\sigma_0]$), since the electromagnetic potential $A$ is currently unmeasurable and can therefore be transformed. I argue that $[A]=[A+d\lambda]_{\lambda}$ and the hoop $[\sigma_0]$ are related by a meaningful duality, so that however one feels about $[A]$ (or any potential $A\in[A]$), it is no worse than $[\sigma_0]$ (or any loop $\sigma_0\in[\sigma_0]$): no ontological firmness is gained by retreating to the loops, which are just as flimsy (...)
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  4. Alexander Afriat, Logic of Gauge.
    The logic of gauge theory is considered by tracing its development from general relativity to Yang-Mills theory, through Weyl's two gauge theories. A handful of elements---which for want of better terms can be called \emph{geometrical justice}, \emph{matter wave}, \emph{second clock effect}, \emph{twice too many energy levels}---are enough to produce Weyl's second theory; and from there, all that's needed to reach the Yang-Mills formalism is a \emph{non-Abelian structure group} (say $\mathbb{SU}\textrm{(}N\textrm{)}$).
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  5. Alexander Afriat, Shortening the Gauge Argument.
    The ''gauge argument'' is often used to 'deduce' interactions from a symmetry requirement. A transition---whose justification can take some effort---from global to local transformations is typically made at the beginning of the argument. But one can spare the trouble by \emph{starting} with local transformations, as global ones do not exist in general. The resulting economy seems noteworthy.
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  6. 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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  7. S. Albeverio, R. Høegh-Krohn & H. Holden (1984). Markov Cosurfaces and Gauge Fields. In Heinrich Mitter & Ludwig Pittner (eds.), Stochastic Methods and Computer Techniques in Quantum Dynamics. Springer-Verlag 211--231.
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  8. 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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  9. Scott Alsid & Mario Serna (2015). Unifying Geometrical Representations of Gauge Theory. Foundations of Physics 45 (1):75-103.
    We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza–Klein theory, those who use Grassmannian models models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school (...)
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  10. J. Anandan (1980). On the Hypotheses Underlying Physical Geometry. Foundations of Physics 10 (7-8):601-629.
    The relationship between physics and geometry is examined in classical and quantum physics based on the view that the symmetry group of physics and the automorphism group of the geometry are the same. Examination of quantum phenomena reveals that the space-time manifold is not appropriate for quantum theory. A different conception of geometry for quantum theory on the group manifold, which may be an arbitrary Lie group, is proposed. This provides a unified description of gravity and gauge fields as well (...)
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  11. 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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  12. 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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  13. Richard Arnowit & Pran Nath (eds.) (1976). Gauge Theories and Modern Field Theory. The MIT Press.
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  14. D. Atkinson, Inelastic Phase-Shift Analysis.
    Phase-shift analysis is a commonly used technique to extract the scattering amplitudes of a two-body strong-interaction scattering process from the experimentally measured quantities | total cross-section, di erential cross-section, polarization and spin-correlation parameters. However, at a xed energy, all the scattering amplitudes can be multiplied by an arbitrary angle-dep phase-factor without a ecting the measurables. It would seem then that the phase of the..
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  15. 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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  16. 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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  17. Guido Bacciagaluppi, Gauge- and Galilei-Invariant Geometric Phases.
    Neither geometric phases nor differences in geometric phases are generally invariant under time-dependent unitary transformations (unlike differences in total phases), in particular under local gauge transformations and Galilei transformations. (This was pointed out originally by Aharonov and Anandan, and in the case of Galilei transformations has recently been shown explicitly by Sjoeqvist, Brown and Carlsen.) In this paper, I introduce a phase, related to the standard geometric phase, for which phase differences are both gauge- and Galilei-invariant, and, indeed, invariant under (...)
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  18. 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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  19. David John Baker (2010). Gauging What's Real: The Conceptual Foundations of Gauge Theories, by Richard Healey. Mind 119 (474):490-494.
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  20. David John Baker, Review of Richard Healey, Gauging What's Real. [REVIEW]
    Review of Richard Healey's 2008 book. To appear in MIND.
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  21. 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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  22. 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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  23. 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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  24. 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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  25. M. Beleggia, Y. Zhu, S. Tandon & M. De Graef (2003). Electron-Optical Phase Shift of Magnetic Nanoparticles II. Polyhedral Particles. Philosophical Magazine 83 (9):1143-1161.
    A method is presented to compute the electron-optical phase shift for a magnetized polyhedral nanoparticle, with either a uniform magnetization or a closure domain . The method relies on an analytical expression for the shape amplitude, combined with a reciprocal-space description of the magnetic vector potential. The model is used to construct two building blocks from which more complex structures can be generated. Phase computations are also presented for the five Platonic and 13 Archimedean solids. Fresnel and Foucault imaging mode (...)
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  26. 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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  27. Gordon Belot (2003). Symmetry and Gauge Freedom. Studies in History and Philosophy of Science Part B 34 (2):189-225.
    The classical field theories that underlie the quantum treatments of the electromagnetic, weak, and strong forces share a peculiar feature: specifying the initial state of the field determines the evolution of some degrees of freedom of the theory while leaving the evolution of some others wholly arbitrary. This strongly suggests that some of the variables of the standard state space lack physical content-intuitively, the space of states of such a theory is of higher dimension than the corresponding space of genuine (...)
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  28. 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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  29. 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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  30. 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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  31. Bernd Binder, Iterative Interplay Between Aharonov-Bohm Deficit Angle and Berry Phase.
    Geometric phases can be observed by interference as preferred scattering directions in the Aharonov-Bohm (AB) effect or as Berry phase shifts leading to precession on cyclic paths. Without curvature single-valuedness is lost in both case. It is shown how the deficit angle of the AB conic metric and the geometric precession cone vertex angle of the Berry phase can be adjusted to restore single-valuedness. The resulting interplay between both phases confirms the non--linear iterative system providing for generalized fine structure constants (...)
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  32. 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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  33. Nazim Bouatta & Jeremy Butterfield (2013). The Emergence of Integrability in Gauge Theories. In Vassilios Karakostas & Dennis Dieks (eds.), Epsa11 Perspectives and Foundational Problems in Philosophy of Science. Springer 229--238.
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  34. 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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  35. 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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  36. 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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  37. 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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  38. 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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  39. 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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  40. 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 this journal, Kosso ([2000]) 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 ([1980]) 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 significance of symmetries, re-analysing (...)
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  41. 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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  42. 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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  43. Tian-Yu Cao (1988). Gauge Theory and the Geometrization of Fundamental Physics. In Harvey R. Brown & Rom Harré (eds.), Philosophical Foundations of Quantum Field Theory. Oxford University Press 117--33.
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  44. 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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  45. 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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  46. 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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  47. 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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  48. Gabriel Catren (2014). On the Relation Between Gauge and Phase Symmetries. Foundations of Physics 44 (12):1317-1335.
    We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s moment (...)
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  49. Gabriel Catren (2008). Geometric Foundations of Classical Yang–Mills Theory. Studies in History and Philosophy of Science Part B 39 (3):511-531.
    We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and relationalism. Using the fiber bundle formulation of Yang-Mills theory, a precise definition of locality is proposed. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a necessary but not sufficient condition for establishing a relational theory of local internal motion. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of (...)
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  50. George F. Chapline (1980). Geometrization of Gauge Fields. In A. R. Marlow (ed.), Quantum Theory and Gravitation. Academic Press 1--177.
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