Lawrence P. Horwitz's Books

Relativistic Classical Mechanics and Electrodynamics

By: Martin Land,Lawrence P. Horwitz

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Relativistic Classical Mechanics and Electrodynamics

By: Martin Land,Lawrence P. Horwitz

This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron. The full apparatus of classical analytical mechanics is generalized to relativistic form by replacing Galilean covariance with manifest Lorentz covariance and introducing a coordinate-independent parameter to play the role of Newton's universal and monotonically advancing time. Fundamental physics is described by the -evolution of a system point through an unconstrained 8D phase space, with mass a dynamical quantity conserved under particular interactions. Classical gauge invariance leads to an electrodynamics derived from five -dependent potentials described by 5D pre-Maxwell field equations. Events trace out worldlines as advances monotonically, inducing pre-Maxwell fields by their motions, and moving under the influence of these fields. The dynamics are governed canonically by a scalar Hamiltonian that generates evolution of a 4D block universe defined at to an infinitesimally close 4D block universe defined at +. This electrodynamics, and its extension to curved space and non-Abelian gauge symmetry, is well-posed and integrable, providing a clear resolution to grandfather paradoxes. Examples include classical Coulomb scattering, electrostatics, plane waves, radiation from a simple antenna, classical pair production, classical CPT, and dynamical solutions in weak field gravitation. This classical framework will be of interest to workers in quantum theory and general relativity, as well as those interested in the classical foundations of gauge theory.

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Page Count

124

Publisher

Springer Nature

Published Date

ISBN 10

3031020790

ISBN 13

9783031020797

Relativistic Many-Body Theory and Statistical Mechanics

By: Lawrence P. Horwitz,Rafael I. Arshansky

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Relativistic Many-Body Theory and Statistical Mechanics

By: Lawrence P. Horwitz,Rafael I. Arshansky

In 1941, E.C.G. Stueckelberg wrote a paper, based on ideas of V. Fock, that established the foundations of a theory that could covariantly describe the classical and quantum relativistic mechanics of a single particle. Horwitz and Piron extended the applicability of this theory in 1973 (to be called the SHP theory) to the many-body problem. It is the purpose of this book to explain this development and provide examples of its applications. We first review the basic ideas of the SHP theory, both classical and quantum, and develop the appropriate form of electromagnetism on this dynamics. After studying the two body problem classically and quantum mechanically, we formulate the N-body problem. We then develop the general quantum scattering theory for the N-body problem and prove a quantum mechanical relativistically covariant form of the Gell-Mann-Low theorem. The quantum theory of relativistic spin is then developed, including spin-statistics, providing the necessary apparatus for Clebsch-Gordan additivity, and we then discuss the phenomenon of entanglement at unequal times. In the second part, we develop relativistic statistical mechanics, including a mechanism for stability of the off-shell mass, and a high temperature phase transition to the mass shell. Finally, some applications are given, such as the explanation of the Lindneret alexperiment, the proposed experiment of Palacios et al which should demonstrate relativistic entanglement (at unequal times), the space-time lattice, low energy nuclear reactions and applications to black hole physics.

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Page Count

145

Publisher

Morgan & Claypool Publishers

Published Date

ISBN 10

1681749475

ISBN 13

9781681749471

Relativistic Quantum Mechanics

By: Lawrence P. Horwitz

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Relativistic Quantum Mechanics

By: Lawrence P. Horwitz

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semi group evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied.

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Page Count

214

Publisher

Springer

Published Date

ISBN 10

9401772614

ISBN 13

9789401772617

Quantum Statistical Mechanics

By: William C. Schieve,Lawrence P. Horwitz

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Quantum Statistical Mechanics

By: William C. Schieve,Lawrence P. Horwitz

Introduces many-body theory of modern quantum statistical mechanics to graduate students in physics, chemistry, engineering and biology.

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Page Count

429

Publisher

Cambridge University Press

Published Date

ISBN 10

0521841461

ISBN 13

9780521841467

Book's by Lawrence P. Horwitz

Relativistic Classical Mechanics and Electrodynamics

Relativistic Classical Mechanics and Electrodynamics

Relativistic Many-Body Theory and Statistical Mechanics

Relativistic Many-Body Theory and Statistical Mechanics

Relativistic Quantum Mechanics

Relativistic Quantum Mechanics

Quantum Statistical Mechanics

Quantum Statistical Mechanics

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