Towards Quantum Noncommutative $κ$-deformed Field Theory

Daszkiewicz, M.; Lukierski, J.; Woronowicz, M.

Towards Quantum Noncommutative $κ$-deformed Field Theory

Authors

Daszkiewicz, M.

Lukierski, J.

Woronowicz, M.

Description

We introduce new $κ$-star product describing the multiplication of quantized $κ$-deformed free fields. The $κ$-deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the $κ$-deformation of field oscillators algebra - we relate these two deformations. We demonstrate that for suitable choice of $κ$-deformed field oscillators algebra the $κ$-deformed version of microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the $κ$-deformed mass shell. We show by constructing the $κ$-deformed Fock space that the use of $κ$-deformed oscillator algebra permits 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 noncommutative quantum $λϕ^4$ field theory. It appears that the classical fourmomentum conservation law is satisfied at the interaction vertices.
LaTeX, 16 pages. V2: some clarifications supplemented, two formulas added. V3: three references added, version in press in Physical Review D