34 found
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  1.  28
    Particles Vs. Events: The Concatenated Structure of World Lines in Relativistic Quantum Mechanics. [REVIEW]R. Arshansky, L. P. Horwitz & Y. Lavie - 1983 - Foundations of Physics 13 (12):1167-1194.
    The dynamical equations of relativistic quantum mechanics prescribe the motion of wave packets for sets of events which trace out the world lines of the interacting particles. Electromagnetic theory suggests thatparticle world line densities be constructed from concatenation of event wave packets. These sequences are realized in terms of conserved probability currents. We show that these conserved currents provide a consistent particle and antiparticle interpretation for the asymptotic states in scattering processes. The relation between current conservation and unitarity is used (...)
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  2.  41
    On the Two Aspects of Time: The Distinction and its Implications. [REVIEW]L. P. Horwitz, R. I. Arshansky & A. C. Elitzur - 1988 - Foundations of Physics 18 (12):1159-1193.
    The contemporary view of the fundamental role of time in physics generally ignores its most obvious characteric, namely its flow. Studies in the foundations of relativistic mechanics during the past decade have shown that the dynamical evolution of a system can be treated in a manifestly covariant way, in terms of the solution of a system of canonical Hamilton type equations, by considering the space-time coordinates and momenta ofevents as its fundamental description. The evolution of the events, as functions of (...)
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  3.  41
    Off-Shell Electromagnetism in Manifestly Covariant Relativistic Quantum Mechanics.David Saad, L. P. Horwitz & R. I. Arshansky - 1989 - Foundations of Physics 19 (10):1125-1149.
    Gauge invariance of a manifestly covariant relativistic quantum theory with evolution according to an invariant time τ implies the existence of five gauge compensation fields, which we shall call pre-Maxwell fields. A Lagrangian which generates the equations of motion for the matter field (coinciding with the Schrödinger type quantum evolution equation) as well as equations, on a five-dimensional manifold, for the gauge fields, is written. It is shown that τ integration of the equations for the pre-Maxwell fields results in the (...)
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  4.  21
    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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  5.  81
    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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  6.  31
    The Landau-Peierls Relation and a Causal Bound in Covariant Relativistic Quantum Theory.R. Arshansky & L. P. Horwitz - 1985 - Foundations of Physics 15 (6):701-715.
    Thought experiments analogous to those discussed by Landau and Peierls are studied in the framework of a manifestly covariant relativistic quantum theory. It is shown that momentum and energy can be arbitrarily well defined, and that the drifts induced by measurement in the positions and times of occurrence of events remain within the (stable) spread of the wave packet in space-time. The structure of the Newton-Wigner position operator is studied in this framework, and it is shown that an analogous time (...)
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  7.  28
    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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  8.  64
    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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  9.  35
    On the Electromagnetic Interaction in Relativistic Quantum Mechanics.L. P. Horwitz - 1984 - Foundations of Physics 14 (10):1027-1046.
    A fundamental problem in the construction of local electromagnetic interactions in the framework of relativistic wave equations of Klein-Gordon or Dirac type is discussed, and shown to be resolved in a relativistic quantum theory of events described by functions in a Hilbert space on the manifold of space-time. The relation, abstracted from the structure of the electromagnetic current, between sequences of events, parametrized by an evolution parameter τ (“historical time”), and the commonly accepted notion of particles is reviewed. As an (...)
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  10.  95
    Equilibrium Relativistic Mass Distribution for Indistinguishable Events.L. Burakovsky & L. P. Horwitz - 1995 - Foundations of Physics 25 (6):785-818.
    A manifestly covariant relativistic statistical mechanics of a system of N indistinguishable events with motion in space-time parametrized by an invariant “historical time” τ is considered. The relativistic mass distribution for such a system is obtained from the equilibrium solution of the generalized relativistic Boltzmann equation by integration over angular and hyperangular variables. All the characteristic averages are calculated. Expressions for the pressure and the energy density are found, and the relativistic equation of state is obtained. Validity criteria are defined. (...)
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  11.  18
    The Covariant Stark Effect.M. C. Land & L. P. Horwitz - 2001 - Foundations of Physics 31 (6):967-991.
    This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire (...)
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  12.  41
    Selection Rules for Dipole Radiation From a Relativistic Bound State.M. C. Land, R. I. Arshansky & L. P. Horwitz - 1994 - Foundations of Physics 24 (4):563-578.
    Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the nonrelativistic Schrödinger energy spectrum. In this paper, we study the radiative transitions of these states in the dipole approximation and find that the selection rules are identical with those of the usual nonrelativistic theory, expressed in a manifestly covariant form. In addition to the transverse and longitudinal polarizations of the nonrelativistic theory, we (...)
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  13.  80
    Relativistic Mass Distribution in Event-Anti-Event System and “Realistic” Equation of State for Hot Hadronic Matter.L. Burakovsky & L. P. Horwitz - 1995 - Foundations of Physics 25 (8):1127-1146.
    We find the equation of state p, ρ ∫ T 6,which gives the value of the sound velocity c 27 = 0.20,in agreement with the “realistic” equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event-anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological (...)
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  14.  55
    Hypercomplex Quantum Mechanics.L. P. Horwitz - 1996 - Foundations of Physics 26 (6):851-862.
    The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a (...)
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  15.  32
    Radiation Reaction of the Classical Off-Shell Relativistic Charged Particle.O. Oron & L. P. Horwitz - 2001 - Foundations of Physics 31 (6):951-966.
    It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham–Lorentz–Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg–Feynman–Schwinger covariant mechanics (the zero mode fields of (...)
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  16.  32
    Schwinger Algebra for Quaternionic Quantum Mechanics.L. P. Horwitz - 1997 - Foundations of Physics 27 (7):1011-1034.
    It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting (...)
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  17.  19
    A First-Order Equation for Spin in a Manifestly Relativistically Covariant Quantum Theory.A. Arensburg & L. P. Horwitz - 1992 - Foundations of Physics 22 (8):1025-1039.
    Relativistic quantum mechanics has been formulated as a theory of the evolution ofevents in spacetime; the wave functions are square-integrable functions on the four-dimensional spacetime, parametrized by a universal invariant world time τ. The representation of states with spin is induced with a little group that is the subgroup of O(3, 1) leaving invariant a timelike vector nμ; a positive definite invariant scalar product, for which matrix elements of tensor operators are covariant, emerges from this construction. In a previous study (...)
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  18.  14
    Chiral Two-Component Spinors and the Factorization of Kramers's Equation.L. C. Biedenharn & L. P. Horwitz - 1984 - Foundations of Physics 14 (10):953-961.
    Kramers's equation specialized to the Coulomb field is factored using a rotationally invariant, angular momentum based, algebra of three anticommuting operators. Comparing the explicit chiral two-component solutions for the factored equation to the two-component solutions defined by the Foldy-Wouthuysen series for the Dirac-Coulomb Hamiltonian, it is concluded that this series cannot converge.
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  19.  87
    On the Equivalence of the Skyrme-Witten Model and Large-N C Quark Models.L. C. Biedenharn & L. P. Horwitz - 1994 - Foundations of Physics 24 (3):401-417.
    We review the equivalence of the two-flavor Skyrme-Witten model and the two-flavor large-N c quark model. The claimed equivalence for three flavorsbetween these two models is shown to be incorrectly given in the literature, and the properly equivalent extended three-flavor large-N c quark model is constructed and discussed.
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  20. Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics.L. Burakovsky & L. P. Horwitz - 1995 - Foundations of Physics 25 (9):1335-1358.
    We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant “historical time” τ. We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann- type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation (...)
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  21.  46
    Relativistic Mass Distribution in Event-Anti-Event System and {OpenQuotes} Realistic {CloseQuotes} Equation of State for Hot Hadronic Matter.L. Burakovsky & L. P. Horwitz - 1995 - Foundations of Physics 25 (8).
  22.  30
    Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory.L. P. Horwitz & Y. Strauss - 1998 - Foundations of Physics 28 (10):1607-1616.
    We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these (...)
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  23.  20
    Preface.L. P. Horwitz, J. R. Fanchi & M. Land - 2005 - Foundations of Physics 35 (7):1113-1115.
  24.  17
    Preface.L. P. Horwitz - 2002 - Foundations of Physics 32 (12):1807-1808.
  25.  15
    Preface.L. P. Horwitz - 2003 - Foundations of Physics 33 (8):1153-1156.
  26.  16
    Preface.L. P. Horwitz - 2007 - Foundations of Physics 37 (4-5):456-459.
  27.  23
    Preface IARD 2008 Proceedings.L. P. Horwitz - 2011 - Foundations of Physics 41 (1):1-3.
  28.  29
    Relativistic Notion of Mass and a Resolution of a Conflict Between Schopenhauer and Hegel.L. P. Horwitz & Ari Belenkiy - 2002 - Foundations of Physics 32 (6):963-979.
    We discuss a mass change that has its origin in the action of forces on an object. This phenomenon, well-known in the context of quantum field theory (mass renormalization), can be discussed systematically in both classical and quantum mechanics in a framework given by Stückelberg. We employ this framework to resolve an interesting conflict of opinions between Schopenhauer and Hegel in the mid-19th century. We show that Hegel, Kant, and Schopenhauer demonstrated remarkable prescience in their views as seen from a (...)
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  29.  67
    Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric.O. Oron & L. P. Horwitz - 2003 - Foundations of Physics 33 (9):1323-1338.
    We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a (...)
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  30.  63
    Relativistic Brownian Motion and Gravity as an Eikonal Approximation to a Quantum Evolution Equation.O. Oron & L. P. Horwitz - 2005 - Foundations of Physics 35 (7):1181-1203.
    We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential to take into account the analytic continuation of “unphysical” fluctuations.
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  31.  37
    The Conformal Metric Associated with the U(1) Gauge of the Stueckelberg–Schrödinger Equation.O. Oron & L. P. Horwitz - 2003 - Foundations of Physics 33 (8):1177-1187.
    We review the relativistic classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelbert–Schrödinger equation. To achieve this, one must introduce a fifth, Lorentz scalar, compensation field, in addition to the four vector fields with compensate the action of the space-time derivatives. A generalized Lorentz force can be derived from the classical Hamilton equations associated with this evolution function. We show that the fifth (scalar) field can be eliminated through the introduction (...)
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  32.  66
    Relativistic Mechanics of Continuous Media.S. Sklarz & L. P. Horwitz - 2001 - Foundations of Physics 31 (6):909-934.
    In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the (...)
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  33.  85
    Representation of the Resonance of a Relativistic Quantum Field Theoretical Lee–Friedrichs Model in Lax–Phillips Scattering Theory.Y. Strauss & L. P. Horwitz - 2000 - Foundations of Physics 30 (5):653-694.
    The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay, law. The Wigner–Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does riot correspond to a semigroup (...)
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  34.  53
    Measurement Theory in the Lax-Phillips Formalism.S. Tasaki, E. Eisenberg & L. P. Horwitz - 1994 - Foundations of Physics 24 (8):1179-1194.
    It is shown that the application of the Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the “Many-Hilbert-Space” theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the decoherence may occur (...)
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