Geometrical Models of the Locally Anisotropic Space-Time

TL;DR

This paper reviews geometric models based on Finsler space-time to explore Lorentz symmetry violation, emphasizing the preservation of relativistic symmetry as a key criterion for effective field theories.

Contribution

It provides a review of Finslerian extensions of relativity theory, highlighting recent developments and the authors' own results in modeling locally anisotropic space-time.

Findings

Finsler geometry offers a framework for Lorentz symmetry violation without breaking relativistic symmetry.

Preservation of relativistic symmetry is crucial for the viability of non-Lorentz-invariant theories.

The paper consolidates recent results on Finsler extensions of relativity theory.

Abstract

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.