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

TL;DR

This paper explores the quantization of field theories with non-abelian, curved momentum spaces, specifically kappa-deformed spaces, revealing how curvature introduces ambiguities similar to curved spacetime quantization.

Contribution

It develops a phase space formulation for particles with group-valued momenta and constructs the quantization framework for kappa-deformed field theories.

Findings

Constructed the one-particle Hilbert space for kappa-deformed phase space

Identified quantization ambiguities due to momentum space curvature

Defined basic field operators and two-point functions for kappa-quantum fields

Abstract

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.