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

In certain scenarios of deformed relativistic symmetries relevant for noncommutative 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 κ-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 κ-quantum fields.