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

M. Daszkiewicz·K. Imilkowska·J. Kowalski-Glikman·S. Nowak
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Abstract

In this paper we recall the construction of scalar field action on $κ$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $κ$-Poincaré 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 $Φ^4$ term we investigate the modified conservation laws. We show that the local interactions on $κ$-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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M. Daszkiewicz, K. Imilkowska, J. Kowalski-Glikman, S. Nowak. 2005-01-11. Scalar field theory on $κ$-Minkowski space-time and Doubly Special Relativity. https://doi.org/10.1142/s0217751x0502238x

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