Lorentz symmetry violation without violation of relativistic symmetry

TL;DR

This paper explores a Finslerian model where Lorentz symmetry is broken by anisotropic fermion-antifermion condensates, yet relativistic symmetry persists through generalized Lorentz boosts, providing a new perspective on symmetry violations.

Contribution

It introduces a Finslerian framework with anisotropic condensates that break Lorentz symmetry while maintaining relativistic symmetry via generalized boosts.

Findings

Lorentz symmetry is broken by anisotropic condensates.

Relativistic symmetry remains valid through generalized Lorentz boosts.

Constructed a Lagrangian for fundamental fields interacting with anisotropic condensate.

Abstract

Within the framework of the Finslerian approach to the problem of violation of Lorentz symmetry, consideration is given to a flat axially symmetric Finslerian space of events, which is the generalization of Minkowski space. Such an event space arises from the spontaneous breaking of initial gauge symmetry and from the formation of anisotropic fermion-antifermion condensate. It is shown that the appearance of an anisotropic condensate breaks Lorentz symmetry; relativistic symmetry, realized by means of the 3-parameter group of generalized Lorentz boosts, remains valid here nevertheless. We have obtained the bispinor representation of the group of generalized Lorentz boosts, which makes it possible to construct the Lagrangian for an interaction of fundamental fields with anisotropic condensate.