Finsler Geometry, Relativity and Gauge Theories
Springer Science & Business Media, 6 de des. 2012 - 370 pàgines
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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Primary Mathematical Definitions
Implications of the Invariance Identities
Significance of the Auxiliary Vector Field from the Viewpoint
Implications of Metric Conditions
Proper Finslerian Gauge Transformations
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Acta Asanov Berwald C. R. Acad Cartan connection Cartan connection coefficients Cartan covariant derivative Christoffel symbols commutation concept condition conformal constructed coordinate system covariant derivative curvature tensor defined definition denotes dependence differentiating direction-dependent equality Euler-Lagrange derivative field variables Finsler geometry Finsler space Finslerian geodesics Finslerian metric function Finslerian metric tensor Finslerschen formulated G-transformations gauge fields gauge tensor gauge transformations gauge-covariant geodesics given by Equation gravitational field gravitational field equations homogeneity hypersurface implies indicatrix invariance identities kinematic Lagrangian density linear manifolds Math Matsumoto Minkowskian motion n-tuples notation obtain orthonormal osculating Pande parametrical representation Phys physical fields Proc PROPOSITION Pure Appl Räumen recurrent Finsler space relation respect Riemannian metric tensor right-hand side Rund Russian S3-like satisfied scalar density Section Singh space-time special relativity spinor static substituting symmetric tangent Minkowskian space tangent vectors tensor density tetrad torsion tensor transformation law Univ vector field velocity yields