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

V. V. Khruschev; A. N. Leznov

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arXiv · hep-th/0207082

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

V. V. Khruschev·A. N. Leznov

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Abstract

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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V. V. Khruschev, A. N. Leznov. 2003-03-06. Relativistic invariant Lie algebras for kinematical observables in quantum space-time. https://arxiv.org/abs/hep-th/0207082

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