Killing Symmetries of Generalized Minkowski Spaces. Part 2: Finite Structure of Space–Time Rotation Groups in Four Dimensions

Abstract

In this paper, we continue the study of the Killing symmetries of an 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 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.