$\kappa$-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

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Cited by in corpus (33)

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• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• On kappa-deformation and triangular quasibialgebra structure
• Covariant particle exchange for kappa-deformed theories in 1+1 dimensions
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• $\kappa$-Deformations and Extended $\kappa$-Minkowski Spacetimes
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Different realizations of kappa-momentum space and relative-locality effect
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Kappa-deformation of phase space; generalized Poincare algebras and R-matrix
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Beyond Fock space in three dimensional semiclassical gravity
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Bicrossproduct construction versus Weyl-Heisenberg algebra
• Quantization of kappa-deformed free fields and kappa-deformed oscillators
• From Noncommutative Sphere to Nonrelativistic Spin
• Noncommutative kappa-Minkowski phi4 theory: Construction, properties and propagation
• Braided algebras and the kappa-deformed oscillators
• The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras
• Three-dimensional gravity and deformations of relativistic symmetries