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

We report a rigorous quantization of topological quantum mechanics on ${\mathbb{R}}_{⩾0}$ 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.