Twisted statistics and the structure of Lie-deformed Minkowski spaces

Abstract

We show that the realizations of noncommutative coordinates that are linear in the Lorentz generators form a closed Lie algebra under certain conditions. The star product and the coproduct for the momentum generators are obtained for these Lie algebras and the corresponding twist satisfies the cocycle and normalization conditions. We also obtain the twisted flip operator and the $\mathcal{R}$-matrix that define the statistics of particles or quantum fields propagating in these noncommutative spacetimes. The Lie algebra obtained in this work contains a special case which has been used in the literature to put bounds on noncommutative parameters from the experimental limits on Pauli forbidden transitions. The general covariant framework presented here is suitable for analyzing the properties of particles or quantum fields at the Planck scale.

6 pages; version accepted for publication in Phys. Rev. D

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• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Twist for Snyder space
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Two-particle system in Coulomb potential for twist-deformed space-time
• Features of description of composite system's motion in twist-deformed space-time
• Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical system