A Note on Quantum Field Theories with a Minimal Length Scale

TL;DR

This paper examines quantum field theories incorporating a minimal length scale, highlighting how such models act as high-energy regulators through higher derivatives and discussing the artifacts introduced by series truncation.

Contribution

It analyzes the low energy limit of these theories and clarifies the nature of extra poles and instabilities as artifacts of series truncation.

Findings

Minimal length acts as a high-energy regulator.

Extra poles are artifacts of series truncation.

Instabilities are linked to higher order derivatives.

Abstract

The aim of this note is to address the low energy limit of quantum field theories with a minimal length scale. The essential feature of these models is that the minimal length acts as a regulator in the asymptotic high energy limit which is incorporated through an infinite series of higher order derivatives. If one investigates a perturbative expansion in inverse powers of the Planck mass, one generically obtains extra poles in the propagator, and instabilities connected with the higher order derivative Lagrangian, that are however artifacts of truncating the series.