Boosts in an arbitrary direction and maximal causal velocities in a deformed Minkowski space

TL;DR

This paper explores how boosts in a deformed Minkowski space, where metric coefficients depend on non-metric coordinates like energy, lead to two possible maximal velocities, with only the anisotropic one being physically meaningful.

Contribution

It derives the general form of boosts in arbitrary directions within a deformed Minkowski space considering space anisotropy and discusses the physical relevance of two maximal velocities.

Findings

Two mathematically possible maximal velocities, isotropic and anisotropic.

Only the anisotropic velocity remains invariant under deformed boosts.

The form of boosts in arbitrary directions is explicitly derived.

Abstract

We discuss boosts in a deformed Minkowski space, i.e. a four-dimensional space-time with metric coefficients depending on non-metric coordinates (in particular on the energy). The general form of a boost in an arbitrary direction is derived in the case of space anisotropy. Two maximal 3-vector velocities are mathematically possible, an isotropic and an anisotropic one. However, only the anisotropic velocity has physical meaning, being invariant indeed under deformed boosts.