Path Intergals and Perturbative Expansions for Non-Compact Symmetric Spaces

TL;DR

This paper develops a method to construct path integrals and perturbation theory for quantum systems on non-compact symmetric spaces, leading to a new exactly solvable model and advancing towards quantum gravity applications.

Contribution

It introduces a novel approach to path integrals on non-compact symmetric spaces with a perturbation theory that preserves global structure, including a new exactly solvable model.

Findings

Constructed path integrals for non-compact symmetric spaces

Developed a global-structure respecting perturbation theory

Derived a new exactly solvable quantum model

Abstract

We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global structure of the system. This perturbation expansion is evaluated for a simple example and leads to a new exactly soluble model. This work is a step towards the construction of a strong coupling perturbation theory for quantum gravity.