Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory

Abstract

Lecture notes for the course "Batalin-Vilkovisky formalism and applications in topological quantum field theory" given at the University of Notre Dame in the Fall 2016 for a mathematical audience. In these lectures we give a slow introduction to the perturbative path integral for gauge theories in Batalin-Vilkovisky formalism and the associated mathematical concepts.

References in corpus (12)

• Deformation quantization of Poisson manifolds, I
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Lie theory for nilpotent L-infinity algebras
• Perturbative quantum gauge theories on manifolds with boundary
• Topological BF Theories in 3 and 4 Dimensions
• Classical and quantum Lagrangian field theories with boundary
• Remarks on Chern-Simons invariants
• Wilson surfaces and higher dimensional knot invariants
• An introduction to the Batalin-Vilkovisky formalism
• Unimodular L-infinity algebras
• Wave relations

Cited by in corpus (10)

• Perspectives on the pure spinor superfield formalism
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity
• General Relativity and the AKSZ construction
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• BV equivalence with boundary
• The geometry of graded cotangent bundles
• Twisted IBL-infinity-algebra and string topology: First look and examples
• A geometric construction of representations of the Berezin-Toeplitz quantization
• An Introduction to Geometric Quantization and Witten's Quantum Invariant
• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons