Batalin-Vilkovisky Formalism in the Functional Approach to Classical Field Theory

2011/01/31 by Klaus Fredenhagen, Katarzyna Rejzner · 3 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Classical field theory #Complex system #Covariance #Differential geometry #Formalism (music) #General covariance #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #Observable #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s00220-012-1487-y

42 pages, improved formulation, typos corrected

arxiv created 2011/07/05 · openalex publication_date 2012/06/30 · openalex created_date 2016/06/24 · arxiv updated 2017/08/23 · openalex updated_date 2026/08/05

Abstract

We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime. In particular, this allows a homological construction of the Poisson algebra of observables in classical gravity. Our methods heavily rely on the differential geometry of configuration spaces of classical fields.

Citations

• On the multisymplectic formalism for first order field theories
• The inverse function theorem of Nash and Moser
• Renormalization of the abelian Higgs-Kibble model
• Batalin–Vilkovisky integrals in finite dimensions
• Local BRST cohomology in gauge theories
• Renormalization of gauge theories
• Is general relativity ‘essentially understood’?
• CLASSICAL FIELD THEORY: ADVANCED MATHEMATICAL FORMULATION
• Commutative Algebra

Cited by

• Effective quantum gravity observables and locally covariant QFT
• Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory
• Coloring Operads for Algebraic Field Theory