Kappa-Minkowski space-time and the star product realizations
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We investigate a Lie algebra-type $ κ$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ κ$-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 $ κ$-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
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