Light-like $\kappa$-deformations and scalar field theory via Drinfeld twist

Abstract

In this article we will use the Drinfeld twist leading to light-like $\kappa$-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 $\kappa$-Poincaré-Hopf algebra. Using this approach we show that there is no problem with formulating integration on $\kappa$-Minkowski space and no need for introducing a new measure. We have shown that the $\star$-product obtained from this twist enables us to define a free scalar field theory on $\kappa$-Minkowski space that is equivalent to a commutative one on a usual Minkowski space. We also discuss the interacting ${\varphi }^4$ scalar field model compatible with $\kappa$-Poincaré-Hopf algebra.

11 pages, accepted for publication in the Proceedings of the NCG parallel session of the conference Conceptual and Technical Challenges in Quantum Gravity 2014 to be published in the Journal of Physics Conference Series

References in corpus (9)

• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Gauge theories on the kappa-Minkowski spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance

Cited by in corpus (11)

• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Spacetime and deformations of special relativistic kinematics
• Twisted statistics and the structure of Lie-deformed Minkowski spaces
• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Associative realizations of $\kappa$-deformed extended Snyder model
• Twisted conformal algebra related to $\kappa$-Minkowski space
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime