$\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law

Abstract

We consider $\kappa$-deformed relativistic symmetries described algebraically by modified Majid-Ruegg bicrossproduct basis and investigate the quantization of field oscillators for the $\kappa$-deformed free scalar fields on $\kappa$-Minkowski space. By modification of standard multiplication rule, we postulate the $\kappa$-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 $\kappa$-deformed Fock space generated by our $\kappa$-deformed oscillators which satisfy the standard algebraic relations with modified $\kappa$-multiplication rule. We show that such a $\kappa$-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of $\kappa$-deformed algebra of oscillators in field-theoretic noncommutative framework.