Homotopy transfer for QFT on non-compact manifold with boundary: a case study

TL;DR

This paper develops a homological perturbation method to construct effective theories for topological quantum mechanics on a half-line, generalizing Feynman graph calculations and exploring boundary transfer in BV algebra structures.

Contribution

It introduces a homological perturbation approach for effective theory construction on non-compact manifolds with boundary, extending BV quantization and illustrating boundary transfer.

Findings

Effective theories fit into derived BV algebra structures

Homological perturbation generalizes Feynman graph computations

Boundary transfer process illustrated in a simple example

Abstract

In this work we report a homological perturbation calculation to construct effective theories of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$. Such calculation can be regarded as a generalization of Feynman graph computation. The resulting effective theories fit into derived BV algebra structure, which generalizes BV quantization. Besides, our construction may serve as the simplest example of a process called "boundary transfer", which may help study bulk-boundary correspondence.