# One-loop analysis with nonlocal boundary conditions

## TL;DR

This paper performs a detailed one-loop analysis of quantum mechanical models with nonlocal boundary conditions, revealing that the zeta(0) value matches that of Robin boundary conditions, and discusses potential applications in quantum field theory and gravity.

## Contribution

It introduces a detailed technique for one-loop calculations with nonlocal boundary conditions, applicable to quantum field theory and gravity.

## Key findings

- zeta(0) matches Robin boundary conditions
- technique applicable to quantum field theory
- potential use in quantum gravity

## Abstract

In the eighties, Schroder studied a quantum mechanical model where the stationary states of Schrodinger's equation obey nonlocal boundary conditions on a circle in the plane. For such a problem, we perform a detailed one-loop calculation for three choices of the kernel characterizing the nonlocal boundary conditions. In such cases, the zeta(0) value is found to coincide with the one resulting from Robin boundary conditions. The detailed technique here developed may be useful for studying one-loop properties of quantum field theory and quantum gravity if nonlocal boundary conditions are imposed.