Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space

Abstract

Unified graded differential algebra, generated by $\kappa$-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with $\kappa$-Poincaré-Hopf algebra. For time- and space-like deformations, the super-Jacobi identities are not satisfied. By introducing additional generator, interpreted as exterior derivative, we find a new unique algebra that satisfies all super-Jacobi identities. It is universal and valid for all type of deformations (time-, space-, and light-like). For time-like deformations this algebra coincides with the one in \cite{sitarz}. Different realizations of our algebra in terms of super-Heisenberg algebra are presented. For light-like deformations we get 4D bicovariant calculus, with $\kappa$-Poincaré-Hopf algebra and present the corresponding twist, which is written in a new covariant way, using Poincaré generators only. In the time- and space-like case this twist leads to $\kappa$-Snyder space. Our results might lead to applications in NC quantum field theories (especially electrodynamics and gauge theories), quantum gravity models, and Planck scale physics.

15 pages, new title, minor changes

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Cited by in corpus (13)

• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Effects of Noncommutativity on the Black Hole Entropy
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Twisted conformal algebra related to $\kappa$-Minkowski space
• The Weyl realizations of Lie algebras and left-right duality
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Maxwell's equations and Lorentz force in doubly special relativity