Kappa-Minkowski space-time and the star product realizations

Abstract

We investigate a Lie algebra-type $\kappa$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $\kappa$-Minkowski space. The coproduct and the star product corresponding to each of them are found. Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $\kappa$-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space.

23 pages, revtex4, no figures, typos corrected, references added; in v3 few references and some comments regarding kappa-Poincare symmetry are included; to appear in EPJC

References in corpus (6)

• A Gravity Theory on Noncommutative Spaces
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Covariant realizations of kappa-deformed space
• Gauge theories on the kappa-Minkowski spacetime
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Action functional for kappa-Minkowski Noncommutative Spacetime

Cited by in corpus (4)

• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Lie algebraic deformations of Minkowski space with Poincare algebra