$\kappa$-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.

LaTeX, 12 pages. V2: second part of chapter 4 changed, new references and comments added. V3: formula (14) corrected. Some additional explanations added. V4: further comments about algebraic structure are added

References in corpus (2)

• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Braided quantum field theories and their symmetries

Cited by in corpus (6)

• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Quantization of kappa-deformed free fields and kappa-deformed oscillators