Generalized kinematical symmetries of quantum phase space

TL;DR

This paper explores generalized kinematical symmetries in quantum phase space, extending traditional algebraic structures with additional constants and invariances in free field equations.

Contribution

It introduces a framework for continuous symmetries generated by quantum observables, generalizing the algebra of quantum phase space with new constants and invariances.

Findings

Invariance of free field equations under generalized symmetries

Extension of the algebra of observables to include additional constants

Demonstration of symmetry structures beyond Lorentz and Heisenberg algebras

Abstract

Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory, that is contained the Lorentz group algebra and the Heisenberg algebra of phase space operators. In the general case commutation relations between observables depend on c, h and additional fundamental constants. Free field equations are considered, which are invariant with respect to generalized kinematical symmetries of the quantum phase space.