Finsler Geometry, Relativity And Gauge Theories (fundamental Theories Of Physics)

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. Front Matter....Pages i-x Front Matter....Pages 1-1 Motivation and Outline of the Book....Pages 3-16 Front Matter....Pages 17-17 Primary Mathematical Definitions....Pages 19-46 Special Finsler Spaces....Pages 47-81 Front Matter....Pages 83-83 Implications of the Invariance Identities....Pages 85-109 Finslerian Approach Based on the Concept of Osculation....Pages 110-151 Parametrical Representation of Physical Fields. The Relevance to Gauge Theories....Pages 152-191 Front Matter....Pages 193-193 Classical Mechanics from the Finslerian Viewpoint....Pages 195-203 Finslerian Refinement of Special Relativity Theory....Pages 204-223 Back Matter....Pages 224-370