Relativistically invariant Lie algebras for kinematic observables in quantum space-time. (English) Zbl 1057.81528

Summary: A deformation of the canonical algebra for kinematic observables of quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistically 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 the general case, the algebra represents a class of Lie algebras, which consists of both simple algebras and semidirect sums of simple and integrable algebras. Some algebras belonging to this class are non-invariant under the \(T\) and \(C\) transformations. Possible applications of obtained algebras for descriptions of states of matter under extreme conditions are briefly discussed.


81R05 Finite-dimensional groups and algebras motivated by physics and their representations
83C45 Quantization of the gravitational field
81T20 Quantum field theory on curved space or space-time backgrounds
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