Relativistic invariant Lie algebras for kinematical observables in   quantum space-time
  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. 
V. V. Khruschev (1), A. N. Leznov (2, 3 and 4) ((1) Department for   Gravitation and Fundamental Metrology VNIIMS, Moscow, R...