Kappa-Minkowski space-time and the star product realizations

Understand

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.