Towards Quantum Noncommutative $\kappa$-deformed Field Theory

Abstract

We introduce 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 suitable choice of $\kappa$-deformed field oscillators algebra the $\kappa$-deformed version of microcausality 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 $\kappa$-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 $\lambda {\varphi }^4$ 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

References in corpus (5)

• Twisted Statistics in kappa-Minkowski Spacetime
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Fock space, quantum fields and kappa-Poincaré symmetries
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Blackbody radiation in κ-Minkowski spacetime

Cited by in corpus (5)

• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Quantization of kappa-deformed free fields and kappa-deformed oscillators