Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-08-11
Phys.Rev.D77:105007,2008
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 16 pages. V2: some clarifications supplemented, two formulas added. V3: three references added, version in press in Phy
Scientific paper
10.1103/PhysRevD.77.105007
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 $\lambda\phi^4$ field theory. It appears that the classical fourmomentum conservation law is satisfied at the interaction vertices.
Daszkiewicz Marcin
Lukierski Jerzy
Woronowicz Mariusz
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