# Relativistic Many-Body Theory and Statistical Mechanics

- Lawrence P. Horwitz, Rafael I Arshansky

- May 2018

### Description

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 dynamic. 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 Lindner

*et al*experiment, 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.

### About Editors

Lawrence Paul Horwitz studied engineering physics at the New York University College of Engineering, and then moved on to Harvard University where he received his doctorate in 1957. He worked at IBM Watson Research Laboratory, The University of Genova, and CERN, before moving to Tel Aviv University. He is currently Professor Emeritus at Tel Aviv University, Bar Ilan University and Ariel University.Rafael Arshansky received his master's from the Lomonosov Moscow State University. He obtained his PhD at Tel Aviv University for his work, "Topics in Relativistic Quantum Theory: Two Body Bound States and Scattering Theory," under the supervision of L P Horwitz. His present fields of interest are the relativistic dynamics of events with any number of degrees of freedom in classical and quantum mechanics, and general relativity.

### Table of Contents

1.Introduction

2. Many Body Relativistic Mechanics and Gauge Theory

3. Quantum Mechanical Two Body Problem and Consequences for Many Body

Systems

4. Scattering Theory

5. Classical Relativistic Statistical Mechanics

6. Quantum Relativistic Statistical Mechanics, Spin Statistics and

Quantum Field Theory

7. Discussion and Outlook### Bibliographic

Paperback ISBN: 9780750329163

Ebook ISBN: 9781681749471

DOI: 10.1088/978-1-6817-4948-8

Publisher: Morgan & Claypool Publishers