Author(s)

V. Balan, G. Yu. Bogoslovsky, S. S. Kokarev, D. G. Pavlov, S. V. Siparov, N. Voicu

“Transilvania” University of Bra?ov, Bra?ov, Romania.
Institute of Hypercomplex Systems in Geometry and Physics, Fryazino, Russia.
Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia.
State University of Civil Aviation, St. Petersburg, Russia.
University Politehnica of Bucharest, Bucharest, Romania.

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

Lorentz-, Poincare- and Gauge Symmetry; Spontaneous Symmetry Breaking; Alternative Gravity Theories; Space-Time Anisotropy; Finsler Differential Geometry

Balan, V. , Bogoslovsky, G. , Kokarev, S. , Pavlov, D. , Siparov, S. and Voicu, N. (2012) Geometrical Models of the Locally Anisotropic Space-Time. Journal of Modern Physics, 3, 1314-1335. doi: 10.4236/jmp.2012.329170.