Anatomy of a deformed symmetry: field quantization on curved momentum space

Details Anatomy of a deformed symmetry: field quantization on curved momentum space Anatomy of a deformed symmetry: field quantization on curved momentum space

2010-09-06

arxiv.org/abs/1009.1097v3

Phys.Rev.D83:025025,2011

Physics

High Energy Physics

High Energy Physics - Theory

RevTeX, 15 pages, no figures. v2 typos corrected and minor cosmetic modifications, v3 to appear on Phys. Rev. D

Scientific paper

10.1103/PhysRevD.83.025025

In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of kappa-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for kappa-quantum fields.

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