Minimal Length Uncertainty Relation and Ultraviolet Regularisation

TL;DR

This paper demonstrates how a minimal length uncertainty relation, inspired by string theory and quantum gravity, can serve as an ultraviolet regularisation in field theory while preserving symmetries.

Contribution

It explicitly shows ultraviolet regularisation via a minimal length scale within the euclidean path integral framework, maintaining rotation and translation invariance.

Findings

Ultraviolet divergences are regularised by the minimal length.

Rotation and translation invariance are preserved.

A detailed example geometry is analyzed.

Abstract

Studies in string theory and quantum gravity suggest the existence of a finite lower limit $\Delta x_0$ to the possible resolution of distances, at the latest on the scale of the Planck length of $10^{-35}m$. Within the framework of the euclidean path integral we explicitly show ultraviolet regularisation in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example geometry is studied in detail.