Space-Time Noncommutativity from Particle Mechanics

Abstract

We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard `commuting' gauge. Therefore the Poisson algebra, and the resulting quantum theory, are identical in the two gauges. The only difference is in the interpretation of space-time coordinates. The procedure is repeated for the case of a coupling with a constant electromagnetic field, where the reparametrization symmetry is preserved. For more arbitrary interactions, we show that standard dynamical system can be rendered noncommutative in space and time by a simple change of variables.

13 pp

References in corpus (2)

• Unitary Quantum Physics with Time-Space Noncommutativity
• Magnetic Backgrounds and Noncommutative Field Theory

Cited by in corpus (23)

• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Topics in Noncommutative Geometry Inspired Physics
• Unitary Quantum Physics with Time-Space Noncommutativity
• GUP-based and Snyder Non-Commutative Algebras, Relativistic Particle models and Deformed Symmetries: A Unified Approach
• $\kappa$-Minkowski Spacetime Through Exotic "Oscillator"
• Particle Dynamics on Snyder space
• Electrodynamics of a Generalized Charged Particle in Doubly Special Relativity Framework
• The $AdS$ particle
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Noncommutative spaces, the quantum of time and the Lorentz symmetry
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Noncommutativity and Reparametrisation symmetry
• Dynamical origin of the ${\star }_{\theta }$-noncommutativity in field theory from quantum mechanics
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Time-Space Noncommutativity And Symmetries For A Massive Relativistic Particle
• Relativistic Particles on Quantum Space-time
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Interacting Relativistic Particle: Time-Space Noncommutativity And Symmetries
• Abelian gerbes as a gauge theory of quantum mechanics on phase space
• The E(2) Particle
• Canonical Quantization, Space-Time Noncommutativity and Deformed Symmetries in Field Theory
• Lie algebraic noncommuting structures from reparametrisation symmetry
• Noncommutativity In A Simple Toy Model