String/Quantum Gravity motivated Uncertainty Relations and Regularisation in Field Theory

TL;DR

This paper reviews how quantum gravity-inspired modifications to uncertainty relations can introduce finite bounds on measurements, leading to natural regularisation mechanisms in quantum field theories.

Contribution

It presents a general framework for path integral formulation on geometries with modified uncertainty relations, highlighting their role in IR and UV regularisation.

Findings

Finite lower bounds on position and momentum resolutions can regularise divergences.

Modified uncertainty relations induce IR and UV regularisation effects.

The framework connects quantum gravity corrections to field theory regularisation.

Abstract

The possibility of the existence of small correction terms to the canonical commutation relations and the uncertainty relations has recently found renewed interest. In particular, such correction terms could induce finite lower bounds $\Delta x_0, \Delta p_0$ to the resolution of distances and/or momenta. I review a general framework for the path integral formulation of quantum field theories on such generalised geometries, and focus then on the mechanisms by which $\Delta p_0>0$, and/or $\Delta x_0>0$ lead to IR and/or UV regularisation.