Finsler Geometry, Relativity and Gauge Theories

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Springer Science & Business Media, 6 de des. 2012 - 370 pàgines
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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.
 

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Continguts

Primary Mathematical Definitions
19
Problems
44
Notes
45
Problems
77
Implications of the Invariance Identities
85
Problems
108
Significance of the Auxiliary Vector Field from the Viewpoint
121
Problems
149
Problems
232
Implications of Metric Conditions
253
Proper Finslerian Gauge Transformations
260
Problems
266
Bibliography
301
Biographies
312
204
320
206
326

GaugeCovariant Derivatives of Spinors and Isospinors
167
Problems
189
Finslerian Refinement of Special Relativity Theory
204
Problems
223
224
332
236
360
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