Killing symmetries of generalized Minkowski spaces. 2-Finite structure of space-time rotation groups

TL;DR

This paper investigates the finite structure of space-time rotation groups in generalized Minkowski spaces with energy-dependent metrics, focusing on four-dimensional cases and deriving explicit forms for deformed Minkowski spaces.

Contribution

It extends the study of Killing symmetries to finite transformations in generalized Minkowski spaces with non-metrical coordinate dependence, especially for deformed Minkowski spaces.

Findings

Derived explicit forms of finite rotations and boosts in deformed Minkowski space.

Analyzed the structure of space-time rotation groups with non-diagonal, energy-dependent metrics.

Focused on four-dimensional space-time, providing specific parametric representations.

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 coordinates. We discuss here the finite structure of the space-time rotations 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), for which we derive the explicit general form of the finite rotations and boosts in different parametric bases.