Concepts in Relativistic Dynamics

The following sections are included:

• Dedication
• Acknowledgments
• Contents

In the past fifty years there have been significant developments in the theory of relativistic mechanics, both classical and and quantum. It is the purpose of this book to explain and emphasize the conceptual foundations of these developments with minimal use of advanced mathematical techniques, so that these ideas will be accessible to a wide range of readers, students and researchers…

The following sections are included:

• Lorentz Group and Covariance
• Mass and Momentum
• Pair Annihilation in Classical Mechanics
• Relativistic Hamilton-Lagrange Dynamics
• The Classical Two Body System
• Some Examples

The following sections are included:

• Introduction to the Quantum Theory: History and Foundations
• Evolution of the Wave Function and Locality
• The Stueckelberg-Horwitz-Piron Quantum Theory
• The Lindner Experiment
• The Landau-Peierls and Newton Wigner Problems

The following sections are included:

• Definition of Spin
• Relativistic Spin and the Dirac Representation
• The Many Body Problem with Spin, and Spin-Statistics
• Construction of the Fock Space and Quantum Field Theory
• Discussion

Models with action at a distance potentials, such as the Coulomb potential and the harmonic oscillator, have been very useful in nonrelativistic mechanics. They provide a simpler framework than the more fundamental field mediated models for interaction, and often provide a good approximation. They are also straightforwardly amenable to rigorous mathematical analysis…

The following sections are included:

• Introduction
• Foundations of Relativistic Scattering Theory
• The S Matrix
• Cross Sections
• Two Body Partial Wave Analysis
• Unitarity and the Levinson Theorem
• Resonances and Semigroup Evolution
• Lax Phillips Theory
• Summary

In this chapter we discuss the general formulation of gauge fields in the quantum theory, both abelian and nonabelian. A generalization of the elementary Stueckelberg diagram (Fig. 1 of Chapter 2), demonstrating a “classical” picture of pair annihilation and creation, provides a similar picture of a process involving two or more vertices (diagrams of this type appear in Feynman’s paper in 1949 [Feynman (1949)] with sharp instantaneous vertices). A single vertex, as it was in Stueckelberg’s original diagram, in the presence of a nonabelian gauge field, can induce a transition to an antiparticle with different identity. Such transitions can result in “flavor oscillations”, such as in the simple case of neutrino oscillations, transitions between electron and muon neutrinos. We shalll discuss this situation briefly here. The construction of the Lorentz force will also be discussed…

In this chapter, we shall discuss the relativistic statistical mechanics of a many body system, for which the points in space time constitute the fundamental entities for which distribution functions must be constructed to achieve a manifestly covariant theory. The counting of events is essentially equivalent to the counting of world lines corresponding to particles. Therefore one should expect that, as we indeed find, the statistical mechanics of events is therefore closely related to the theory of statistical mechanics of particles, as developed, for example, in Synge [Synge (1957); see also, de Groot (1980)]. We construct a canonical Gibbs ensemble based on a microcanonical ensemble, enabling us to define a temperature and the basic thermodynamic functions [Horwitz (1981)]…

The following section is included:

• References