Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity

Details Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity

2004-10-06

arxiv.org/abs/hep-th/0410058v3

Int.J.Mod.Phys. A20 (2005) 4925-4940

Physics

High Energy Physics

High Energy Physics - Theory

17 pages; some editing done, final version to be published in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X0502238X

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.

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