Killing Symmetries of Generalized Minkowski Spaces. I. Algebraic-Infinitesimal Structure of Spacetime 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 coordinates. 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
- Publication:
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Foundations of Physics
- Pub Date:
- April 2004
- DOI:
- arXiv:
- arXiv:hep-th/0505088
- Bibcode:
- 2004FoPh...34..617C
- Keywords:
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- generalized Minkowski spaces;
- Killing equations;
- infinitesimal generators;
- generalized Poincaré algebra;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 35 pages. Slightly improved version with respect to the published one (some misprints corrected, Ref.s added, Eq.s revised, comments made)