NONCOMMUTATIVE QUANTUM CONFORMAL PLANE-WAVE DEFORMATION

We construct a q-deformation of the plane wave as a formal power serie s in the noncommutative coordinates of q-Minkowski space-time and four -momenta. This q-plane wave has analogous properties to the classical one, in particular, it has the properties of q-Lorentz covariance, and it satisfies the q-d'Alembert equation (proposed earlier by one of us ) on the q-Lorentz covariant momentum cone. On the other hand, this q- plane wave is not an exponent or q-exponent. Thus, it differs conceptu ally from the classical plane wave and may serve as a its regularizati on. We also give the polynomial solutions of the q-d'Alembert equation , (C) 1998 Published by Elsevier Science B.V. All rights reserved.