2002/07/31 by V. V. Khruschev, A. N. Leznov
Physics and Astronomy · #hep-th
published as Grav.Cosmol. 9 (2003) 159 · 7 pages, LaTeX2e, misprints corrected, references added, discussion enlarged
arxiv created 2003/03/06 · arxiv updated 2009/11/30
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.