Perturbative BV-BFV formalism with homotopic renormalization: a case study

TL;DR

This paper presents a rigorous perturbative BV-BFV quantization of topological quantum mechanics on intervals, extending Costello's homotopic renormalization and comparing different state interpretations.

Contribution

It extends Costello's homotopic renormalization within the BV-BFV formalism and connects it to previous BV quantization approaches for topological quantum mechanics.

Findings

Successful rigorous quantization of topological quantum mechanics on intervals.

Extension of homotopic renormalization within BV-BFV formalism.

Comparison of different state interpretations in BV and BV-BFV frameworks.

Abstract

We report a rigorous quantization of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$ and $\mathbf{I}= [0, 1]$ in perturbative BV-BFV formalism. Costello's homotopic renormalization is extended, and incorporated in our construction. Moreover, BV quantization of the same model studied in our previous work is derived from the BV-BFV quantization, leading to a comparison between different interpretations of ''state'' in these two frameworks.