13 research outputs found
Differential forms and k-Minkowski spacetime from extended twist
We analyze bicovariant differential calculus on -Minkowski spacetime.
It is shown that corresponding Lorentz generators and noncommutative
coordinates compatible with bicovariant calculus cannot be realized in terms of
commutative coordinates and momenta. Furthermore, -Minkowski space and
NC forms are constructed by twist related to a bicrossproduct basis. It is
pointed out that the consistency condition is not satisfied. We present the
construction of -deformed coordinates and forms (super-Heisenberg
algebra) using extended twist. It is compatible with bicovariant differential
calculus with -deformed -Hopf algebra. The extended
twist leading to -Poincar\'{e}-Hopf algebra is also discussed.Comment: 15 pages, minor typos corrected to match the published versio
Twist for Snyder space
We construct the twist operator for the Snyder space. Our starting point is a
non-associative star product related to a Hermitian realisation of the
noncommutative coordinates originally introduced by Snyder. The corresponding
coproduct of momenta is non-coassociative. The twist is constructed using a
general definition of the star product in terms of a bi-differential operator
in the Hopf algebroid approach. The result is given by a closed analytical
expression. We prove that this twist reproduces the correct coproducts of the
momenta and the Lorentz generators. The twisted Poincar\'{e} symmetry is
described by a non-associative Hopf algebra, while the twisted Lorentz symmetry
is described by the undeformed Hopf algebra. This new twist might be important
in the construction of different types of field theories on Snyder space.Comment: 15 pages, references added, matches published versio
Toward the classification of differential calculi on κ-Minkowski space and related field theories
Classification of differential forms on κ-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 κ-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 κ-Poincar\'e 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
Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
We propose two families of differential algebras of classical dimension on
kappa-Minkowski space. The algebras are constructed using realizations of the
generators as formal power series in a Weyl super-algebra. We also propose a
novel realization of the Lorentz algebra so(1,n-1) in terms of Grassmann-type
variables. Using this realization we construct an action of so(1,n-1) on the
two families of algebras. Restriction of the action to kappa-Minkowski space is
covariant. In contrast to the standard approach the action is not Lorentz
covariant except on constant one-forms, but it does not require an extra
cotangent direction.Comment: 16 page