Localization and diffusion in polymer quantum field theory

TL;DR

This paper investigates how polymer quantization, inspired by quantum gravity, affects localization and diffusion in quantum field theory, revealing unique physical features distinct from other Planck-scale models.

Contribution

It provides a detailed analysis of localization and diffusion properties in polymer quantum field theory, highlighting differences from models with space-time discreteness.

Findings

Localization is only mildly affected by polymer effects.

Polymer diffusion significantly differs from dimensional reduction in other models.

Polymer quantization introduces a characteristic scale with unique physical implications.

Abstract

Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.