On Information Theory, Spectral Geometry and Quantum Gravity

TL;DR

This paper reveals a profound connection between information theory and spectral geometry, leading to new insights into quantum gravity, including a finite formulation of quantum field theory on curved space with safe removal of infrared cutoff.

Contribution

It establishes a novel link between information theory and spectral geometry, providing a finite approach to quantum field theory on curved space with ultraviolet and infrared cutoffs.

Findings

Ultraviolet cutoff bounds spatial information density.

Path integral reduces to finite integrals with both cutoffs.

Infrared cutoff removal is mathematically safe.

Abstract

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.