General relativity and the AKSZ construction

DOI10.1007/s00220-021-04127-6zbMath1470.81055arXiv2006.13078OpenAlexW3036188108MaRDI QIDQ2041640

G. Canepa, Michele Schiavina, Alberto Sergio Cattaneo

Publication date: 23 July 2021

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.13078

zbMATH Keywords

torsionquantizationEinstein-Hilbert theoryAlexandrov-Kontsevich-Schwarz-Zaboronski (AKSZ) constructionBatalin-Vilkovysky formalismPalatini-Cartan theory

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) Gravitational interaction in quantum theory (81V17) Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Methods of quantum field theory in general relativity and gravitational theory (83C47) Analysis on supermanifolds or graded manifolds (58C50) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Equations in function spaces; evolution equations (58D25)

Related Items (3)

BV equivalence with boundary ⋮ Gravitational constraints on a lightlike boundary ⋮ Presymplectic AKSZ formulation of Einstein gravity

Cites Work

• Unnamed Item
• Elimination of the auxiliary fields in the antifield formalism
• Quantum gravity from the point of view of locally covariant quantum field theory
• Classical BV theories on manifolds with boundary
• Parent formulation at the Lagrangian level
• On time
• First order parent formulation for generic gauge field theories
• BV equivalence between triadic gravity and BF theory in three dimensions
• BFV-complex and higher homotopy structures
• Homological reduction of constrained Poisson algebras
• The reduced phase space of Palatini-Cartan-Holst theory
• Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
• Local BRST cohomology in the antifield formalism. I: General theorems
• Globalization for perturbative quantization of nonlinear split AKSZ sigma models on manifolds with boundary
• Towards holography in the BV-BFV setting
• A cellular topological field theory
• Two-dimensional Yang-Mills theory on surfaces with corners in Batalin-Vilkovisky formalism
• Perturbative quantum gauge theories on manifolds with boundary
• Path-integral equivalence between the extended and nonextended Hamiltonian formalisms
• BV-BFV approach to general relativity: Palatini-Cartan-Holst action
• The Geometry of the Master Equation and Topological Quantum Field Theory
• BV-BFV approach to general relativity: Einstein-Hilbert action
• Frame-like Lagrangians and presymplectic AKSZ-type sigma models
• Split Chern–Simons Theory in the BV-BFV Formalism
• GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY
• Quantum Theory of Gravity. I. The Canonical Theory
• A generalized canonical formalism and quantization of reducible gauge theories

This page was built for publication: General relativity and the AKSZ construction