Classical and quantum Lagrangian field theories with boundary

Understand

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.