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

Abstract

We report a rigorous quantization of topological quantum mechanics on R 0 and 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 previous work [WY22] is derived from the BV-BFV quantization, leading to a comparison between different interpretations of "state" in these two frameworks.