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$κ$-Deformed Statistics and Classical Fourmomentum Addition Law

M. Daszkiewicz·J. Lukierski·M. Woronowicz
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Abstract

We consider $κ$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $κ$-deformed free scalar fields on $κ$-Minkowski space. By modification of standard multiplication rule, we postulate the $κ$-deformed algebra of bosonic creation and annihilation operators. Our algebra permits to define the n-particle states with classical addition law for the fourmomenta in a way which is not in contradiction with the nonsymmetric quantum fourmomentum coproduct. We introduce $κ$-deformed Fock space generated by our $κ$-deformed oscillators which satisfy the standard algebraic relations with modified $κ$-multiplication rule. We show that such a $κ$-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of $κ$-deformed algebra of oscillators in field-theoretic noncommutative framework.

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M. Daszkiewicz, J. Lukierski, M. Woronowicz. 2008-02-05. $κ$-Deformed Statistics and Classical Fourmomentum Addition Law. https://doi.org/10.1142/s021773230802673x

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