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  1. Duality in Off-Shell Electromagnetism.Martin Land - 2005 - Foundations of Physics 35 (7):1245-1262.
    In this paper, we examine the Dirac monopole in the framework of Off-Shell Electromagnetism, the five-dimensional U(1) gauge theory associated with Stueckelberg–Schrodinger relativistic quantum theory. After reviewing the Dirac model in four dimensions, we show that the structure of the five-dimensional theory prevents a natural generaliza tion of the Dirac monopole, since the theory is not symmetric under duality transforma tions. It is shown that the duality symmetry can be restored by generalizing the electromagnetic field strength to an element of (...)
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  • Discrete Symmetries of Off-Shell Electromagnetism.Martin Land - 2005 - Foundations of Physics 35 (7):1263-1288.
    This paper discusses the discrete symmetries of off-shell electromagnetism, the Stueckelberg–Schrodinger relativistic quantum theory and its associated 5D local gauge theory. Seeking a dynamical description of particle/antiparticle interactions, Stueckelberg developed a covariant mechanics with a monotonically increasing Poincaré-invariant parameter. In Stueckelberg’s framework, worldlines are traced out through the parameterized evolution of spacetime events, which may advance or retreat with respect to the laboratory clock, depending on the sign of the energy, so that negative energy trajectories appear as antiparticles when the (...)
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  • Theories of Variable Mass Particles and Low Energy Nuclear Phenomena.Mark Davidson - 2014 - Foundations of Physics 44 (2):144-174.
    Variable particle masses have sometimes been invoked to explain observed anomalies in low energy nuclear reactions (LENR). Such behavior has never been observed directly, and is not considered possible in theoretical nuclear physics. Nevertheless, there are covariant off-mass-shell theories of relativistic particle dynamics, based on works by Fock, Stueckelberg, Feynman, Greenberger, Horwitz, and others. We review some of these and we also consider virtual particles that arise in conventional Feynman diagrams in relativistic field theories. Effective Lagrangian models incorporating variable mass (...)
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  • Particles and Events in Classical Off-Shell Electrodynamics.M. C. Land - 1997 - Foundations of Physics 27 (1):19-41.
    Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical. Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical (...)
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  • Relativistic Spin on the Poincaré Group.Ludger Hannibal - 1997 - Foundations of Physics 27 (1):43-56.
    Classical spinning particles are interpreted in terms of an underlying geometric theory. They are described by trajectories on the Poincaré group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2, C)×U(1)×SU(2) gauge theory, unifying gravity and the pre-Higgs standard model. The relation to parametrized relativistic quantum theory is discussed.
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  • Flat Spacetime Gravitation with a Preferred Foliation.J. B. Pitts & W. C. Schieve - 2001 - Foundations of Physics 31 (7):1083-1104.
    Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional “parametrized” and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on τ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, (...)
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  • Coulomb Potential From Lorentz Invariance in N Dimensions.Martin Land - 2007 - Foundations of Physics 37 (4-5):597-631.
    Although Maxwell theory is O(3,1)-covariant, electrodynamics only transforms invariantly between Lorentz frames for special forms of the field, and the generator of Lorentz transformations is not generally conserved. Bérard, Grandati, Lages, and Mohrbach have studied the O(3) subgroup, for which they found an extension of the rotation generator that satisfies the canonical angular momentum algebra in the presence of certain Maxwell fields, and is conserved by the classical motion. The extended generator depends on the field strength, but not the potential, (...)
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  • Hamiltonian Map to Conformal Modification of Spacetime Metric: Kaluza-Klein and TeVeS. [REVIEW]Lawrence Horwitz, Avi Gershon & Marcelo Schiffer - 2011 - Foundations of Physics 41 (1):141-157.
    It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence in this way (...)
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  • Off-Shell Fields and Pauli-Villars Regularization.J. Frastai & L. P. Horwitz - 1995 - Foundations of Physics 25 (10):1495-1510.
    We analyze the correspondence between a five-dimensional U(1)gauge invariant theory and four-dimensional scalar QED, where the fifth dimension (τ)is an invariant parameter of evolution of the manifestly covariant one-particle sector as well as for the full Fock space. The correspondence is represented by the limit in which the width of the photon mass distribution Δs tends to zero and large τ correlations occur. In the limiting procedure, calculation of a twopoint diagram shows that the PauliVillars regularization is intrinsically related to (...)
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  • Relativity Theory: What is Reality? [REVIEW]Diederik Aerts - 1996 - Foundations of Physics 26 (12):1627-1644.
    In classical Newtonian physics there was a clear understanding of “what reality is.≓ Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in “the present.≓ Often it is stated that three-dimensional space and one-dimensional time hare been substituted by four-dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that which is “present,≓ cannot be retained. Is reality then the (...)
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  • Green's Functions for Off-Shell Electromagnetism and Spacelike Correlations.M. C. Land & L. P. Horwitz - 1991 - Foundations of Physics 21 (3):299-310.
    The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and “proper time” τ. The Maxwell theory is contained in this theory; integration of the field equations over τ restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations (...)
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  • Review of Invariant Time Formulations of Relativistic Quantum Theories. [REVIEW]J. R. Fanchi - 1993 - Foundations of Physics 23 (3):487-548.
    The purpose of this paper is to review relativistic quantum theories with an invariant evolution parameter. Parametrized relativistic quantum theories (PRQT) have appeared under such names as constraint Hamiltonian dynamics, four-space formalism, indefinite mass, micrononcausal quantum theory, parametrized path integral formalism, relativistic dynamics, Schwinger proper time method, stochastic interpretation of quantum mechanics and stochastic quantization. The review focuses on the fundamental concepts underlying the theories. Similarities as well as differences are highlighted, and an extensive bibliography is provided.
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  • On the Definition and Evolution of States in Relativistic Classical and Quantum Mechanics.L. P. Horwitz - 1992 - Foundations of Physics 22 (3):421-450.
    Some of the problems associated with the construction of a manifestly covariant relativistic quantum theory are discussed. A resolution of this problem is given in terms of the off mass shell classical and quantum mechanics of Stueckelberg, Horwitz and Piron. This theory contains many questions of interpretation, reaching deeply into the notions of time, localizability and causality. A proper generalization of the Maxwell theory of electromagnetic interaction, required for the well-posed formulation of dynamical problems of systems with electromagnetic interaction is (...)
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