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

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.

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

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• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Quantum particles in non-commutative space-time: an identity crisis
• UV dimensional reduction to two from group valued momenta
• Localization and diffusion in polymer quantum field theory
• A Stochastic Origin of Spacetime Non-Commutativity
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Entanglement entropy, scale-dependent dimensions and the origin of gravity
• Formal developments in curved momentum space: the quantum field theory roadmap
• Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory