Two-dimensional quantum Yang-Mills theory with corners

TL;DR

This paper reformulates 2D quantum Yang-Mills theory into a TQFT-like framework, extending it to include corners and proposing an axiomatic system that could be applicable to higher-dimensional quantum field theories.

Contribution

It introduces a flexible axiomatic formulation of 2D quantum Yang-Mills theory that incorporates corners and aims to generalize to higher dimensions.

Findings

Extended the solution to include corners in the TQFT framework

Proposed an axiomatic system inspired by Schrödinger-Feynman quantization

Discussed physical concepts like unitarity, vacuum, and Wilson loops

Abstract

The solution of quantum Yang-Mills theory on arbitrary compact two-manifolds is well known. We bring this solution into a TQFT-like form and extend it to include corners. Our formulation is based on an axiomatic system that we hope is flexible enough to capture actual quantum field theories also in higher dimensions. We motivate this axiomatic system from a formal Schroedinger-Feynman quantization procedure. We also discuss the physical meaning of unitarity, the concept of vacuum, (partial) Wilson loops and non-orientable surfaces.