Non-commutative space-time and the uncertainty principle

Abstract

The full algebra of relativistic quantum mechanics (Lorentz plus Heisenberg) is unstable. Stabilization by deformation leads to a new deformation parameter $\epsilon {\ell }^2$, $\ell$ being a length and $\epsilon$ a $\pm$ sign. The implications of the deformed algebras for the uncertainty principle and the density of states are worked out and compared with the results of past analysis following from gravity and string theory.

11 pages Latex

Cited by in corpus (11)

• Review of the Phenomenology of Noncommutative Geometry
• Generalized Quantum Relativistic Kinematics: a Stability Point of View
• Some consequences of a noncommutative space-time structure
• Noncommutative correction to the entropy of Schwarzschild black hole with GUP
• Noncommutative correction to the entropy of BTZ black hole with GUP
• The deformation-stability fundamental length and deviations from c
• Space-time: Commutative or noncommutative ?
• Entropy bound for the photon gas in noncommutative spacetime
• Local Currents for a Deformed Algebra of Quantum Mechanics with a Fundamental Length Scale
• The geometry of noncommutative space-time
• An extended Dirac equation in noncommutative space-time