Classical Relativistic Many-Body Dynamics / Edition 1

by M.A. Trump, W.C. Schieve

Overview

in this work, we must therefore assume several abstract concepts that hardly need defending at this point in the history of mechanics. Most notably, these include the concept of the point particle and the concept of the inertial observer. The study of the relativistic particle system is undertaken here by means of a particular classical theory, which also exists on the quantum level, and which is especially suited to the many-body system in flat spacetime. In its fundamental postulates, the theory may be consid­ ered to be primarily the work of E.C.G. Stiickelberg in the 1940's, and of L.P. Horwitz and C. Piron in the 1970's, who may be said to have provided the generalization of Stiickelberg's theory to the many-body system. The references for these works may be found in Chapter 1. The theory itself may be legitimately called off-shell Hamiltonian dynamics, parameterized relativistic mechanics, or even classical event dynamics. The most important feature of the theory is probably the use of an invariant world time parameter, usually denoted T, which provides an evolution time for the system in such as way as to allow manifest co­ variance within a Hamiltonian formalism. In general, this parameter is neither a Lorentz-frame time, nor the proper time of the particles in the system.

Product Details

ISBN-13:	9789048152322
Publisher:	Springer Netherlands
Publication date:	10/12/2011
Series:	Fundamental Theories of Physics , #103
Edition description:	Softcover reprint of the original 1st ed. 1999
Pages:	370
Product dimensions:	6.69(w) x 9.61(h) x 0.03(d)

Table of Contents

1 Introduction.- 2 Frame-Dependent Kinematics.- 3 Covariant Kinematics.- 4 The Dynamical Theory.- 5 The Lagrangian-Hamiltonian Theory.- 6 The Coulomb Potential (I).- 7 The Coulomb Potential (II).- 8 Conclusions and Suggestions.- A The Geometry of World Lines.- A.1 The Geometry of 1-d Curves.- A.1.3 Applications to Nonrelativistic Motion.- A.1.4 Applications to Relativistic Motion.- A.2 Spacetime Curves.- A.2.1 Special Relativistic Kinematics.- A.2.2 World Lines as Regular Curves.- A.2.3 The Unit Binormal Four-Vector.- A.2.4 The Unit Trinormal and Orthonormal Tetrad.- A.3 The Covariant Serret-Frenet Equations.- A.4 The Active Lorentz Transformation.- A.4.1 The Fermi-Walker Operator.- A.4.2 The General Co-Moving Frame.- A.5 Conclusions.- B The Solutions Derived by Cook.- C The No Interaction Theorem.- C.1 Comments on the Proof.- D Classical Pair Annihilation.

Editorial Reviews

‘...this book offers a very nice and fairly self-contained introduction to the subject of classical relativistic dynamics, which will certainly be of interest to graduate students in physics, and to all scientists whose research involves aspects of special relativity theory.'
Mathematical Reviews 2002e

From the Publisher