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

Conceptual and Technical Challenges for Quantum Gravity 2014 – Parallel session: Noncommutative Geometry and Quantum Gravity

Juri, Tajron^1 ; Meljanac, Stjepan^2 ; Samsarov, Andjelo^2

Rudjer Bokovi Institute, Theoretical Physics Division, Bijenika c.54, Zagreb

HR-10002, Croatia^1

Dipartimento di Matematica e Informatica, Universita di Cagliari, INFN, viale Merello 92, Cagliari, Sezione di Cagliari

09123, Italy^2

关键词: Hopf algebras;    Minkowski space;    Scalar field models;    Scalar field theory;    Star products;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/634/1/012005/pdf
DOI  :  10.1088/1742-6596/634/1/012005

来源: IOP

【 摘 要 】

In this article we will use the Drinfeld twist leading to light-like κ-deformations of Poincaréalgebra. 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 us to define a free scalar field theory on κ-Minkowski space that is equivalent to a commutative one on a usual Minkowski space. We also discuss the interacting φ4scalar field model compatible with κ-Poincaré-Hopf algebra.