Killing symmetries of generalized Minkowski spaces. 1-Algebraic-infinitesimal structure of space-time rotation groups

Abstract

In this paper, we introduce the concept of 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. This is the first of a series of papers devoted to the investigation of the Killing symmetries of generalized Minkowski spaces. In particular, we discuss here the infinitesimal-algebraic structure of the space-time rotations in such spaces. It is shown that the maximal Killing group of these spaces is the direct product of a generalized Lorentz group and a generalized translation group. We derive the explicit form of the generators of the generalized Lorentz group in the self-representation and their related, generalized Lorentz algebra. The results obtained are specialized to the case of a 4-dimensional, ''deformed'' Minkowski space , i.e. a pseudoeuclidean space with metric coefficients depending on energy.

arXiv comment35 pages. Slightly improved version with respect to the published one (some misprints corrected, Ref.s added, Eq.s revised, comments made)

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