Tensor Operators in Noncommutative Quantum Mechanics

TL;DR

This paper explores the implications of treating noncommutativity parameters as operators in quantum mechanics, leading to a consistent algebra and rotationally invariant theories with dynamic noncommutativity.

Contribution

It introduces a framework where noncommutativity parameters are operators, expanding the algebra and enabling dynamics in the noncommutative sector.

Findings

Established a consistent algebra with operator-valued noncommutativity

Constructed rotationally invariant theories in this framework

Enabled dynamics for the noncommutativity operator sector

Abstract

Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which permits us to construct theories that are dynamically invariant under the action of the rotation group. In this framework it is also possible to give dynamics to the noncommutativity operator sector, resulting in new features.