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

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Cited by in corpus (11)

• Twisted Statistics in kappa-Minkowski Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Lie algebraic deformations of Minkowski space with Poincare algebra