GUP, Lorentz Invariance (Non)-Violation, and Non-Commutative Geometry

TL;DR

This paper explores how a generalized uncertainty principle affects Lorentz invariance and its connection to non-commutative geometry, analyzing potential violations and restrictions on operator modifications.

Contribution

It formulates a generalized uncertainty principle with modified operators and examines implications for Lorentz invariance and non-commutative geometry models.

Findings

Lorentz invariance constrains operator modifications.

Connections established between uncertainty principles and non-commutative geometry.

Potential conditions under which Lorentz symmetry is preserved or violated.

Abstract

In this work, we formulate a generalized uncertainty principle with both position and momentum operators modified from their canonical forms. We study whether Lorentz symmetry is violated and whether it can be saved with these modifications. The requirement that Lorentz invariance is not violated places restrictions on the way the position and momentum operators can be modified. We also investigate the connection between general uncertainty principle and non-commutative geometry models, e.g.,laying out the connection between area/area operators and angular momentum in both models.