Finsler Geometry, Relativity and Gauge Theories

by G.S. Asanov

Overview

The methods of differential geometry have been so completely merged nowadays with physical concepts that general relativity may well be considered to be a physical theory of the geometrical properties of space-time. The general relativity principles together with the recent development of Finsler geometry as a metric generalization of Riemannian geometry justify the attempt to systematize the basic techniques for extending general relativity on the basis of Finsler geometry. It is this endeavour that forms the subject matter of the present book. Our exposition reveals the remarkable fact that the Finslerian approach is automatically permeated with the idea of the unification of the geometrical space-time picture with gauge field theory - a circumstance that we try our best to elucidate in this book. The book has been written in such a way that the reader acquainted with the methods of tensor calculus and linear algebra at the graduate level can use it as a manual of Finslerian techniques orientable to applications in several fields. The problems attached to the chapters are also intended to serve this purpose. This notwithstanding, whenever we touch upon the Finslerian refinement or generalization of physical concepts, we assume that the reader is acquainted with these concepts at least at the level of the standard textbooks, to which we refer him or her.

Product Details

ISBN-13:	9789027719607
Publisher:	Springer Netherlands
Publication date:	10/31/1985
Series:	Fundamental Theories of Physics , #12
Edition description:	1985
Pages:	370
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

A. Motivation and Outline of the Book.- B. Introduction to Finsler Geometry.- 1/Primary Mathematical Definitions.- 2/Special Finsler Spaces.- C. Basic Equations.- 3/Implications of the Invariance Identities.- 4/Finslerian Approach Based on the Concept of Osculation.- 5/Parametrical Representation of Physical Fields. The Relevance to Gauge Theories.- D. Additional Observations.- 6/Classical Mechanics from the Finslerian Viewpoint.- 7/Finslerian Refinement of Special Relativity Theory.- Concluding Remark.- Appendix A Direction-Dependent Connection and Curvature Forms.- Problems.- Notes.- Appendix B/ General Gauge Field Equations Associated with Curved Internal Space.- B. 1. Introduction.- B. 2. The Parametrical Representation.- B. 3. Associated Gauge Tensors.- B. 4. Identities Satisfied by the Gauge Tensors.- B. 5. Variational Principle for the Parametrical Gauge Fields.- B. 6. General Gauge-Covariant Physical Field Equations.- B. 8. Implications of Metric Conditions.- B. 9. Specification of the Internal Metric Tensor.- B.10. Transition to the Parametrical Finslerian Limit.- B.11. Proper Finslerian Gauge Transformations.- B.12. Flat Internal Space.- Problems.- Note.- Solutions of Problems.- List of Publications on Finsler Geometry.- Biographies.

Editorial Reviews

'... Asanov's book is an important contribution to the literature and should benefit both experts and novices in applications of Finsler geometry.'
Mathematics Abstracts, 576:7 (1986)

From the Publisher