Killing symmetries of generalized Minkowski spaces. 3-Space-time translations in four dimensions

TL;DR

This paper investigates the symmetries of generalized four-dimensional Minkowski spaces with energy-dependent metrics, focusing on translations and their implications for deformed spacetime models.

Contribution

It extends the study of Killing symmetries to four-dimensional generalized Minkowski spaces with non-diagonal, energy-dependent metrics, specifically analyzing translations.

Findings

Derived translation symmetries for four-dimensional generalized Minkowski spaces.

Specialized results to deformed Minkowski space with energy-dependent metrics.

Enhanced understanding of spacetime symmetries in non-standard geometries.

Abstract

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e. a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coodinates. We discuss here the translations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional case. In particular, the results obtained are specialized to the case of a ''deformed'' Minkowski space $\widetilde{M_{4}}$ (i.e. a pseudoeuclidean space with metric coefficients depending on energy).