On the algebraic approach to GUP in anisotropic space
arXiv:2302.04170 · doi:10.1088/1361-6382/acb9cc
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.
arXiv commentAccepted for publication in Classical and Quantum Gravity
References in corpus (31)
- Lorentz-Violating Extension of the Standard Model
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- CPT Violation and the Standard Model
- Data Tables for Lorentz and CPT Violation
- Gravity, Lorentz Violation, and the Standard Model
- A Generalized Uncertainty Principle in Quantum Gravity
- Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
- The algebraic structure of the generalized uncertainty principle
- Electrodynamics with Lorentz-violating operators of arbitrary dimension
- Nonpointlike Particles in Harmonic Oscillators
- Fermions with Lorentz-violating operators of arbitrary dimension
- Generalized Uncertainty Principle: Approaches and Applications
- What Do We Know About Lorentz Invariance?
- A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
- GUP parameter from quantum corrections to the Newtonian potential
- Review on Generalized Uncertainty Principle
- Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
- New Approach to Nonperturbative Quantum Mechanics with Minimal Length Uncertainty
- Lorentz violation and generalized uncertainty principle
- Canonical Transformations in Quantum Mechanics
- Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details
- Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
- On the quasi-position representation in theories with a minimal length
- Quantum Canonical Transformations: Physical Equivalence of Quantum Theories
- Quantum theory of the Generalised Uncertainty Principle
- Unsharp Degrees of Freedom and the Generating of Symmetries
- Optimal uncertainty relations in a modified Heisenberg algebra
- Path integral action in the generalized uncertainty principle framework
- Modified entropies as the origin of generalized uncertainty principles
- Constraining GUP Models Using Limits on SME Coefficients
- A framework for nonrelativistic isotropic models based on generalized uncertainty principles