Introduction to the BV-BFV formalism

Abstract

These notes give an introduction to the mathematical framework of the Batalin-Vilkovisky and Batalin-Fradkin-Vilkovisky formalisms. Some of the presented content was given as a mini course by the first author at the 2018 QSPACE conference in Benasque.

arXiv comment63 pages, 10 figures, minor changes made (added some references, corrected some typos and some small mistakes)

References in corpus (17)

• Deformation quantization of Poisson manifolds, I
• The Geometry of the Master Equation and Topological Quantum Field Theory
• A path integral approach to the Kontsevich quantization formula
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Higher-dimensional Algebra and Topological Quantum Field Theory
• Geometry of Batalin-Vilkovisky quantization
• Perturbative quantum gauge theories on manifolds with boundary
• Classical BV theories on manifolds with boundary
• Poisson sigma models and symplectic groupoids
• Introduction to supergeometry
• Poisson sigma models and deformation quantization
• From local to global deformation quantization of Poisson manifolds
• Predictivity and Nonrenormalizability
• The Poisson sigma model on closed surfaces
• Relational symplectic groupoids
• Relational Symplectic Groupoid Quantization for Constant Poisson Structures

Cited by in corpus (12)

• Covariant canonical formulations of classical field theories
• BV equivalence with boundary
• On Globalized Traces for the Poisson Sigma Model
• Gravity with torsion as deformed $BF$ theory
• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• 4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
• Out-of-time-order asymptotic observables are quasi-isomorphic to time-ordered amplitudes
• 3D Supergravity in the Batalin-Vilkovisky Formalism
• Convolution algebras for Relational Groupoids and Reduction
• Equivariant BV-BFV Formalism
• Self-normalizing Path Integrals