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It is by now well established that the momentum space associated with the non-commutative κ-Minkowski space is a submanifold of de Sitter space. It has been noted recently that field theories built on such momentum space suffer from a subtle form of Lorentz symmetry breaking. Namely, for any negative energy mode the allowed range of rapidities is bounded above. In this paper we construct a complex scalar field theory with a modified action of Lorentz generators which avoids this problem. For such theory we derive conserved charges corresponding to translational and U(1) symmetries. We also discuss in some detail the inner product and Hilbert space structure of the κ-deformed complex quantum field.
Arzano et al. (Mon,) studied this question.
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