# Covariant bandlimitation from Generalized Uncertainty Principles

## TL;DR

This paper explores Lorentz-covariant modifications of the uncertainty principle to incorporate a minimum length scale in quantum field theory, resulting in covariant bandlimitation but with limited effectiveness as a regulator for some quantities.

## Contribution

It introduces a covariant bandlimitation approach based on generalized uncertainty principles, maintaining Lorentz invariance while addressing the minimum length scale.

## Key findings

- Covariant bandlimitation naturally arises from the generalized uncertainty principle.
- The approach does not effectively regulate entanglement entropy.
- Potential applicability in regulating interactions remains open.

## Abstract

It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken. Here we examine a class of Lorentz-covariant generalizations of the uncertainty principle which aim to provide an effective low-energy model for a Lorentz-invariant minimum length. We show how this modification leads to a covariant bandlimitation of quantum field theory. However, we argue that this does not yield an adequate regulator for many quantities of interest, e.g., the entanglement entropy between spatial regions. The possibility remains open that it could aid in regulating interactions.