Finsler Geometry, Relativity and Gauge TheoriesSpringer 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. |
Continguts
Primary Mathematical Definitions | 19 |
Problems | 44 |
Problems | 90 |
Problems | 108 |
Notes | 109 |
Problems | 149 |
17 | 155 |
62 | 162 |
Problems | 223 |
Problems | 232 |
Associated Gauge Tensors | 239 |
General GaugeCovariant Physical Field Equations | 246 |
Implications of Metric Conditions | 253 |
Proper Finslerian Gauge Transformations | 260 |
Solutions of Problems | 266 |
301 | |
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Frases i termes més freqüents
Acta Cienc Asanov Berwald Berwald-Moór metric function C. R. Acad Cartan connection Christoffel symbols condition connection coefficients coordinate system covariant derivative curvature tensor defined definition denotes differential direction-dependent Euler-Lagrange derivative field variables Finsler geometry Finsler manifolds Finsler space Finslerian geodesics Finslerian metric function Finslerian metric tensor finslérienne Finslerschen formulated gauge fields gauge tensor gauge transformations gauge-covariant gravitational field equations homogeneity hypersurface implies indicatrix inertial frame Inst invariance identities K₁ kinematic Kumar L₁ Lagrangian density Lincei Rend linear Math Matsumoto Minkowski Misra Moór motion n-tuples notation obtain Pande Phys physical fields Proc PROPOSITION Pure Appl Räumen recurrent Finsler space relation respect Riemannian metric Riemannian metric tensor right-hand side Rund Russian scalar density Section Singh space-time special relativity spinor subspace substituting symmetric tensor density tensor fields tetrad theory torsion tensor transformation law Univ vanish vector field velocity yields