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 (M) over tilde (4) 6, i.e., a pseudoeuclidean space with metric coefficients depending on energy.

Cardone F, Marrani A, & Mignani R (2004). Killing symmetries of generalized Minkowski spaces. I. Algebraic-infinitesimal structure of spacetime rotation groups. FOUNDATIONS OF PHYSICS, 34(4), 617-641 [10.1023/B:FOOP.0000019628.97334.f0].

Killing symmetries of generalized Minkowski spaces. I. Algebraic-infinitesimal structure of spacetime rotation groups

MIGNANI, ROBERTO
2004

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 (M) over tilde (4) 6, i.e., a pseudoeuclidean space with metric coefficients depending on energy.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/132433
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