On the algebraic approach to GUP in anisotropic space.

Abstract

Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investi- gations 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.