Relativistic invariant Lie algebras for kinematical observables in quantum space-time

Details Relativistic invariant Lie algebras for kinematical observables in quantum space-time Relativistic invariant Lie algebras for kinematical observables in quantum space-time

2002-07-09

arxiv.org/abs/hep-th/0207082v5

Grav.Cosmol. 9 (2003) 159

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, LaTeX2e, misprints corrected, references added, discussion enlarged

Scientific paper

A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on additional fundamental constants M, L and H with the dimensions of mass, length and action, respectively. In some limiting cases the algebra goes over into the well-known Snyder or Yang algebras. In general case the algebra represents a class of Lie algebras, that consists of simple algebras and semidirect sums of simple algebras and integrable ones. Some algebras belonging to this class are noninvariant under T and C transformations. Possible applications of obtained algebras for descriptions of states of matter under extreme conditions are briefly discussed.

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