Towards Quantum Noncommutative $κ$-deformed Field Theory

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dc.creatorDaszkiewicz, M.
dc.creatorLukierski, J.
dc.creatorWoronowicz, M.
dc.date2007-08-11
dc.date2008-03-26
dc.date.accessioned2026-07-07T11:41:49Z
dc.date.available2026-07-07T11:41:49Z
dc.descriptionWe 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.
dc.descriptionLaTeX, 16 pages. V2: some clarifications supplemented, two formulas added. V3: three references added, version in press in Physical Review D
dc.identifierhttps://arxiv.org/abs/0708.1561
dc.identifierhttp://arxiv.org/abs/0708.1561
dc.identifierPhys.Rev.D77:105007,2008
dc.identifierdoi:10.1103/PhysRevD.77.105007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200670
dc.subjectHigh Energy Physics - Theory
dc.titleTowards Quantum Noncommutative $κ$-deformed Field Theory
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