Quantum Abelian Yang-Mills Theory on Riemannian Manifolds with Boundary

TL;DR

This paper develops a functorial quantization of abelian Yang-Mills theory on Riemannian manifolds with boundary, providing an axiomatic, boundary-aware approach within the framework of general boundary quantum field theory.

Contribution

It introduces a novel axiomatic and functorial method for quantizing abelian Yang-Mills theory on manifolds with boundary, extending the general boundary QFT framework.

Findings

Constructed classical solution spaces as axiomatic data.

Developed a functorial quantization procedure.

Achieved a boundary-compatible quantum field theory formulation.

Abstract

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to manifolds. Second, the quantum theory is constructed from the classical axiomatic data in a functorial manner. The target is general boundary quantum field theory, a TQFT-type axiomatic formulation of quantum field theory.