Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy

TL;DR

This paper investigates observable 3-velocities in a flat Finslerian event space with broken 3D isotropy, arising from vacuum condensates that alter space-time geometry and symmetry.

Contribution

It introduces a method to determine observable 3-velocities in an entirely anisotropic Finslerian space with broken 3D isotropy, expanding understanding of space-time symmetry violations.

Findings

Derived the form of the light cone in anisotropic Finslerian space.

Developed a correct norm for rapidities in this space.

Demonstrated how anisotropy affects observable velocities.

Abstract

We study the geometric phase transitions that accompany the dynamic rearrangement of vacuum under spontaneous violation of initial gauge symmetry. The rearrangement may give rise to condensates of three types, namely the scalar, axially symmetric, and entirely anisotropic condensates. The flat space-time keeps being the Minkowski space in the only case of scalar condensate. The anisotropic condensate having arisen, the respective anisotropy occurs also in space-time. In this case the space-time filled with axially symmetric condensate proves to be a flat relativistically invariant Finslerian space with partially broken 3D isotropy, while the space-time filled with entirely anisotropic condensate proves to be a flat relativistically invariant Finslerian space with entirely broken 3D isotropy. The two Finslerian space types are described briefly in the extended introduction to the work, while the original part of the latter is devoted to determining observable 3-velocities in the entirely anisotropic Finslerian event space. The main difficulties that are overcome in solving that problem arose from the nonstandard form of the light cone equation and from the necessity of correct introducing of a norm in the linear vector space of rapidities.