Euclidean Quantum Gravity in Light of Spectral Geometry

TL;DR

This paper reviews recent advances in spectral geometry and their implications for boundary-value problems in Euclidean quantum gravity, emphasizing gauge invariance and boundary conditions in the context of quantum cosmology.

Contribution

It introduces new insights into boundary-value problems in Euclidean quantum gravity using spectral geometry techniques, focusing on gauge-invariant conditions and boundary effects.

Findings

Heat-kernel asymptotics for Laplacian with various boundary conditions

Analysis of gauge-invariant boundary conditions in quantum gravity

Comparison of local and non-local boundary-value problems

Abstract

A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral geometry, i.e. heat-kernel asymptotics for the Laplacian in the presence of Dirichlet, or Robin, or mixed boundary conditions; completely gauge-invariant boundary conditions in Euclidean quantum gravity; local vs. non-local boundary-value problems in one-loop Euclidean quantum theory via path integrals.