$\kappa$--deformed Wigner construction of relativistic wave functions and free fields on $\kappa$-Minkowski space

Abstract

We describe the extension of the Wigner`s infinite-dimensional unitary representations of Poincaré group to the case of $\kappa$-deformed Poincaré group. We show that the corresponding coordinate wave functions on noncommutative space-time are described by free field equations on $\kappa$-deformed Minkowski space. The cases of Klein--Gordon, Dirac, Proca and Maxwell fields are considered. Finally some aspects of second quantization are also discussed.

LaTeX2e, 14 pages. Talk given by J.L. at the D.V. Volkov Memorial Conference "Supersymmetry and Quantum Field Theory", Kharkov, 25-29 July 2000, to be published in Nuclear Physics B Conference Supplements