Towards quantum noncommutative κ-deformed field theory

We introduce a new kappa-star product describing the multiplication of quantized kappa-deformed free fields. The kappa deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the kappa deformation of field oscillators algebra; we relate these two deformations. We demonstrate that for a suitable choice of kappa-deformed field oscillators algebra, the kappa-deformed version of the micro-causality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the kappa-deformed mass shell. We show by constructing the kappa-deformed Fock space that the use of the kappa-deformed oscillator algebra permits one to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of n fields, which for n = 4 defines the interaction vertex in perturbative description of the noncommutative quantum lambda phi(4) field theory. It appears that the classical four-momentum conservation law is satisfied at the interaction vertices.