Light-like κ-deformations and scalar field theory via Drinfeld twist

@article{Juric2015LightlikeA,
  title={Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist},
  author={Tajron Juri'c and Stjepan Meljanac and Andjelo Samsarov},
  journal={Journal of Physics: Conference Series},
  year={2015},
  volume={634}
}
In this article we will use the Drinfeld twist leading to light-like κ-deformations of Poincaré algebra. We shall apply the standard Hopf algebra methods in order to define the star-product, which shall be used to formulate a scalar field theory compatible with κ-Poincaré-Hopf algebra. Using this approach we show that there is no problem with formulating integration on κ-Minkowski space and no need for introducing a new measure. We have shown that the ★-product obtained from this twist enables… 

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References

SHOWING 1-10 OF 44 REFERENCES

SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

We investigate the properties of κ-Minkowski space–time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg–Weyl algebra. The deformed algebra consists of

Universal κ-Poincaré covariant differential calculus over κ-Minkowski space

Unified graded differential algebra, generated by κ-Minkowski noncommutative (NC) coordinates, Lorentz generators and anticommuting one-forms, is constructed. It is compatible with κ-Poincare–Hopf

D ec 2 00 8 κ-Minkowski spacetime as the result of Jordanian twist deformation

Two one-parameter families of twists providing κ−Minkowski ∗−product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspect

kappa-Minkowski spacetime as the result of Jordanian twist deformation

Two one-parameter families of twists providing {kappa}-Minkowski * product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two

κ-Minkowski spacetime and the star product realizations

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of

Kappa-Minkowski spacetime, kappa-Poincaré Hopf algebra and realizations

We unify κ-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincaré algebras are defined. They

κ-deformation of phase space; generalized Poincaré algebras and R-matrix

A bstractWe deform a phase space (Heisenberg algebra and corresponding coalgebra) by twist. We present undeformed and deformed tensor identities that are crucial in our construction. Coalgebras for

Deformed oscillator algebras and QFT in κ-Minkowski spacetime

In this paper, we study the deformed statistics and oscillator algebras of quantum fields defined in $\ensuremath{\kappa}$-Minkowski spacetime. The twisted flip operator obtained from the twist

Gauge theories on the $\kappa$-Minkowski spacetime

Abstract.This study of gauge field theories on $\kappa$-deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed

Twisting all the way: From classical mechanics to quantum fields

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss