Classical and quantum Lagrangian field theories with boundary

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.

24 pages

References in corpus (2)

• On the Classification of Topological Field Theories
• Variations on Homological Reduction

Cited by in corpus (32)

• Perturbative quantum gauge theories on manifolds with boundary
• Multiple Derived Lagrangian Intersections
• Lagrangian structures on mapping stacks and semi-classical TFTs
• A higher stacky perspective on Chern-Simons theory
• The reduced phase space of Palatini-Cartan-Holst theory
• Boundary structure of General Relativity in tetrad variables
• Two-Dimensional Yang-Mills Theory on Surfaces With Corners in Batalin-Vilkovisky Formalism
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Covariant canonical formulations of classical field theories
• On time
• Semiclassical quantization of classical field theories
• Relational symplectic groupoids and Poisson sigma models with boundary
• Groupoids and Poisson sigma models with boundary
• General Relativity and the AKSZ construction
• Combinatorial Quantum Field Theory and Gluing Formula for Determinants
• Constrained systems, generalized Hamilton-Jacobi actions, and quantization
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Wave relations
• Shifted symplectic reduction of derived critical loci
• Two-dimensional perturbative scalar QFT and Atiyah-Segal gluing
• A Lie-Rinehart algebra in general relativity
• Coisotropic submanifolds and dual pairs
• Canonical Functions and Differential Graded Symplectic Pairs in Supergeometry and AKSZ Sigma Models with Boundary
• Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism
• Dirichlet to Neumann operator for abelian Yang-Mills gauge fields
• General Boundary Formulation for $n$-Dimensional Classical Abelian Theory with Corners
• Groupoids, Frobenius algebras and Poisson sigma models
• Covariant Hamiltonian first order field theories with constraints on manifolds with boundary: the case of Hamiltonian dynamics
• Theta Invariants of lens spaces via the BV-BFV formalism
• Harmonic Maps and the Symplectic Category
• Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism