New Kernels in Quantum Gravity

TL;DR

This paper explores non-local boundary conditions in Euclidean quantum gravity and gauge theories, introducing pseudo-differential operators to ensure gauge invariance and extending the framework to Maxwell theory.

Contribution

It proposes a novel scheme for gauge-invariant non-local boundary conditions using pseudo-differential operators in quantum gravity and gauge theories.

Findings

Boundary conditions involve pseudo-differential operators with gauge invariance.

The scheme ensures gauge invariance for ghost and gauge fields.

Extension of the approach to Euclidean Maxwell theory.

Abstract

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a two-by-two matrix of pseudo-differential operators with pseudo-homogeneous kernels. The request of invariance of such boundary conditions under infinitesimal gauge transformations leads to non-local boundary conditions on ghost fields. In Euclidean quantum gravity, an alternative scheme is proposed, where non-local boundary conditions and the request of their complete gauge invariance are sufficient to lead to gauge-field and ghost operators of pseudo-differential nature. The resulting boundary conditions have a Dirichlet and a pseudo-differential sector, and are pure Dirichlet for the ghost. This approach is eventually extended to Euclidean Maxwell theory.