Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics

TL;DR

This paper develops a Hilbert space framework for q-deformed relativistic quantum mechanics, representing the algebra of observables using differential operators on quantum Minkowski space, with a focus on spin-zero particles.

Contribution

It introduces a novel Hilbert space representation of the q-deformed Lorentz algebra where the mass squared operator is diagonal, advancing the mathematical foundation of q-deformed relativistic quantum theories.

Findings

Successfully constructed a differential operator representation on quantum Minkowski space.

Established a Hilbert space where the mass squared operator is diagonal.

Provided a framework for q-deformed relativistic quantum mechanics with spin zero.

Abstract

Using a representation of the q-deformed Lorentz algebra as differential operators on quantum Minkowski space, we define an algebra of observables for a q-deformed relativistic quantum mechanics with spin zero. We construct a Hilbert space representation of this algebra in which the square of the mass $ p^2 $ is diagonal.