Unstable geodesics and topological field theory

TL;DR

This paper employs topological field theory to analyze the cohomology of mapping spaces, linking it with BRST cohomology and physical Hilbert space, and demonstrates the approach with a simple example.

Contribution

It introduces a novel method connecting topological field theory with the cohomology of mapping spaces and BRST cohomology, providing new insights into physical Hilbert spaces.

Findings

Cohomology of mapping space identified with BRST cohomology

Coboundary operator related to tunneling between vacua

Method illustrated through a simple example

Abstract

A topological field theory is used to study the cohomology of mapping space. The cohomology is identified with the BRST cohomology realizing the physical Hilbert space and the coboundary operator given by the calculations of tunneling between the perturbative vacua. Our method is illustrated by a simple example.