Symmetries of fundamental interactions in quantum phase space

TL;DR

This paper explores the generalized symmetries in quantum phase space arising from noncommutative algebra of quantum operators, highlighting their implications for fundamental particle interactions under Lorentz invariance.

Contribution

It introduces a framework for understanding symmetries in quantum phase space that depend on fundamental physical constants, extending traditional symmetry concepts.

Findings

Generalized symmetries depend on mass, length, and action constants.

Lorentz invariance constrains the algebra of quantum operators.

Implications for fundamental interactions are discussed.

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.