Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories

Abstract

Classification of differential forms on $\kappa$-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the $\kappa$-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to $\kappa$-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

arXiv comment37 pages, major revision, new section added, accepted for publication in JHEP

References in corpus (43)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum Spacetime Phenomenology
• Extension of the Cosmic-Ray Energy Spectrum Beyond the Predicted Greisen-Zatsepin-Kuz'min Cutoff
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• A Gravity Theory on Noncommutative Spaces
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Noncommutative Geometry and Gravity
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Observation of Supernova Remnant IC443 with the Fermi Large Area Telescope
• Quantum $\kappa$-Poincare in Any Dimensions
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Kappa-Minkowski space-time and the star product realizations
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• New realizations of Lie algebra kappa-deformed Euclidean space
• Noncommutative Differential Calculus on the Kappa-Minkowski Space
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Constraints on the quantum gravity scale from kappa - Minkowski spacetime
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Gravity induced from quantum spacetime
• Scalar field propagation in the phi^4 kappa-Minkowski model
• Classification of Differential Calculi on U_q(b+), Classical Limits, and Duality
• Noncommutative Symmetries and Gravity
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Non-Pauli Transitions From Spacetime Noncommutativity
• Star product realizations of kappa-Minkowski space
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential calculi on quantum Minkowski space
• Non-Pauli Effects from Noncommutative Spacetimes
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Scalar Field theory in $\kappa$-Minkowski spacetime from twist
• Differential forms and k-Minkowski spacetime from extended twist
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• The bicovariant differential calculus on the kappa-Poincare and kappa-Weyl groups

Cited by in corpus (28)

• The $\kappa$-(A)dS noncommutative spacetime
• Observables and Dispersion Relations in k-Minkowski Spacetime
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Minimal and maximal lengths from position-dependent noncommutativity
• Effects of quantum deformation on the integer quantum Hall effect
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Associative realizations of $\kappa$-deformed extended Snyder model
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Noncommutative correction to the entropy of charged BTZ black hole
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Twisted conformal algebra related to $\kappa$-Minkowski space
• The Weyl realizations of Lie algebras and left-right duality
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Twist for Snyder space
• Central tetrads and quantum spacetimes
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Two-particle system in Coulomb potential for twist-deformed space-time
• A Stochastic Origin of Spacetime Non-Commutativity
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• 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
• Generalization of Weyl realization to a class of Lie superalgebras
• Maxwell's equations and Lorentz force in doubly special relativity