Quantum fields, Noether charges and \kappa-spacetime symmetries

TL;DR

This paper explores the symmetries of ppa-Minkowski non-commutative spacetime using ppa-Poincare9 Hopf algebra, extending Noether analysis, and proposes new methods for quantizing ppa-fields based on their symplectic structure.

Contribution

It generalizes Noether analysis in ppa-deformed spacetime and introduces a novel approach to canonical quantization of ppa-fields.

Findings

Extended Noether charges for ppa-translational symmetries.

Clarified ambiguities in symmetry actions within ppa-framework.

Proposed new quantization method based on symplectic structure.

Abstract

We discuss how the symmetries of $\kappa$-Minkowski non-commutative spacetime can be described by the $\kappa$-Poincar\'e Hopf algebra. In particular, we focus on a generalization of the Noether analysis in the $\kappa$-deformed framework which allows us to introduce Noether charges associated with translational symmetries and makes possible to overcome the apparent ambiguities that seemed to be associated with the action of such symmetries. Moving from the classical to the quantum framework, we will first review past results on path integral quantization of a scalar self-interacting field. We will then show how recent work on the symplectic structure of classical $\kappa$-fields suggests a new approach to the canonical quantization of free fields and and present some new results.