Classical and quantum Lagrangian field theories with boundary

TL;DR

This paper introduces Lagrangian field theories with boundaries, discussing classical aspects and cohomological formalisms (BV and BFV) to handle singularities, aiming for a consistent combination suitable for quantization.

Contribution

It demonstrates how BV and BFV formalisms can be integrated for boundary field theories, facilitating perturbative quantization.

Findings

Unified BV and BFV formalisms for boundary theories

Resolution of singularities in bulk and boundary

Framework for perturbative quantization of boundary theories

Abstract

This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV and the BFV formalisms, respectively) are recalled. One of the goals here (and in [arXiv:1201.0290]) is to show how the latter two formalisms can be put together in a consistent way, also in view of perturbative quantization.