Symmetries of fundamental interactions in quantum phase space

Abstract

Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance condition, the algebra of observables, including Lorentz group generators, depends on additional fundamental physical constants with the dimensions of mass, length and action. Generalized symmetries in a quantum phase space and some consequences for fundamental interactions of particles are considered.