On Information Theory, Spectral Geometry and Quantum Gravity

Understand

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.