A note on gluing via fiber products in the (classical) BV-BFV formalism

TL;DR

This paper explores the process of gluing spacetime manifolds in classical field theory using fiber products within the BV-BFV formalism, providing explicit constructions in various examples.

Contribution

It explicitly constructs the homotopy equivalence of fiber products of field spaces in the BV-BFV formalism for several examples.

Findings

Explicit homotopy constructions for fiber products in BV-BFV formalism

Clarification of gluing procedures in classical field theory

Examples illustrating the fiber product approach

Abstract

In classical field theory, gluing spacetime manifolds along boundary corresponds to taking a fiber product of the corresponding spaces of fields (as differential graded Fr\'echet manifolds) up to homotopy. We construct this homotopy explicitly in several examples in the setting of BV-BFV formalism (Batalin--Vilkovisky formalism with cutting--gluing).