κ-DEFORMED STATISTICS AND CLASSICAL FOUR-MOMENTUM ADDITION LAW
We consider κ-deformed relativistic symmetries described algebraically by modified Majid–Ruegg bi-cross-product 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 one to define the n-particle states with classical addition law for the four-momentum in a way which is not in contradiction with the nonsymmetric quantum four-momentum co-product. 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.