Twists, realizations and Hopf algebroid structure of kappa-deformed phase space

Abstract

The quantum phase space described by Heisenberg algebra possesses undeformed Hopf algebroid structure. The $\kappa$-deformed phase space with noncommutative coordinates is realized in terms of undeformed quantum phase space. There are infinitely many such realizations related by similarity transformations. For a given realization we construct corresponding coproducts of commutative coordinates and momenta (bialgebroid structure). The $\kappa$-deformed phase space has twisted Hopf algebroid structure. General method for the construction of twist operator (satisfying cocycle and normalization condition) corresponding to deformed coalgebra structure is presented. Specially, twist for natural realization (classical basis) of $\kappa$-Minkowski spacetime is presented. The cocycle condition, $\kappa$-Poincaré algebra and $R$-matrix are discussed. Twist operators in arbitrary realizations are constructed from the twist in the given realization using similarity transformations. Some examples are presented. The important physical applications of twists, realizations, $R$-matrix and Hopf algebroid structure are discussed.

34 pages, revised version, accepted in IJMPA

References in corpus (35)

• A Gravity Theory on Noncommutative Spaces
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Fock space, quantum fields and kappa-Poincaré symmetries
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Noncommutative D=4 gravity coupled to fermions
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Deformed General Relativity
• Hydrogen atom on curved noncommutative space
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• Noncommutative BTZ Black Hole and Discrete Time
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• $\kappa$-Deformed Statistics and Classical Fourmomentum Addition Law
• Newton's Equation on the kappa space-time and the Kepler problem
• 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
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• Differential Structure on kappa-Minkowski Spacetime Realized as Module of Twisted Weyl Algebra
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Low-energy constraints on kappa-Minkowski extension of the Standard Model
• Different realizations of kappa-momentum space and relative-locality effect
• Differential forms and k-Minkowski spacetime from extended twist
• Noncommutative fluid dynamics in the Snyder space-time
• Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
• Plane waves in noncommutative fluids

Cited by in corpus (29)

• Noncommutative Spaces and Poincaré Symmetry
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• Noncommutative duality and fermionic quasinormal modes of the BTZ black hole
• Toward the classification of differential calculi on $\kappa$-Minkowski space and related field theories
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Effects of Noncommutativity on the Black Hole Entropy
• Remarks on simple interpolation between Jordanian twists
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Lie algebra type noncommutative phase spaces are Hopf algebroids
• Minimal and maximal lengths from position-dependent noncommutativity
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Twisted conformal algebra related to $\kappa$-Minkowski space
• Noncommutativity and the Weak Cosmic Censorship
• Quantum space and quantum completeness
• Twist for Snyder space
• 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
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• Generalization of Weyl realization to a class of Lie superalgebras
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics
• Maxwell's equations and Lorentz force in doubly special relativity
• Hopf algebroids with balancing subalgebra