On the algebraic approach to GUP in anisotropic space

TL;DR

This paper investigates algebraic models of the generalized uncertainty principle (GUP) in anisotropic space, emphasizing invariance and independence criteria to ensure unambiguous physical descriptions, revealing constraints on such models.

Contribution

It establishes key invariance and independence criteria for algebraic GUP models in anisotropic space and identifies restrictions necessary for consistent formulations.

Findings

Certain GUP models do not satisfy invariance under canonical transformations.

Physical independence of position and momentum constrains GUP algebraic formulations.

Restrictions are placed on how GUP models can be constructed algebraically in anisotropic space.

Abstract

Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investigations on generalized uncertainty principle (GUP) models in anisotropic space, in this paper we identify GUP models satisfying two criteria: (i) invariance of commutators under canonical transformations, and (ii) physical independence of position and momentum on the ordering of auxiliary operators in their definitions. Compliance of these criteria is fundamental if one wishes to unambiguously describe GUP using an algebraic approach but, surprisingly, neither is trivially satisfied when GUP is assumed within anisotropic space. As a consequence, we use these criteria to place important restrictions on what or how GUP models may be approached algebraically.