Fun from none: deformed symmetries and Fock space

TL;DR

This paper introduces deformations of relativistic symmetries, focusing on the $ppa$-deformed scalar quantum field, and explores how these deformations affect the structure of quantum field Hilbert spaces and potential physical implications.

Contribution

It provides a pedagogical overview of deformed relativistic symmetries and constructs the $ppa$-Fock space, highlighting new features and physical consequences of symmetry deformation.

Findings

Deformed Leibnitz rule for translation generators

Richer structure of $ppa$-Fock space

Potential physical implications of symmetry deformation

Abstract

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibnitz rule. We explore the richer structure of the $\kappa$-Fock space and point out possible physical consequences of the deformation.