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

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.