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 \({\widetilde M}\) 4, i.e., a pseudoeuclidean space with metric coefficients depending on energy.
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Cardone, F., Marrani, A. & Mignani, R. Killing Symmetries of Generalized Minkowski Spaces. I. Algebraic-Infinitesimal Structure of Spacetime Rotation Groups. Foundations of Physics 34, 617–641 (2004). https://doi.org/10.1023/B:FOOP.0000019628.97334.f0
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DOI: https://doi.org/10.1023/B:FOOP.0000019628.97334.f0