Axiomatic quantum field theory in terms of operator product expansions: general framework, and perturbation theory via Hochschild cohomology

DOI10.3842/SIGMA.2009.090zbMath1188.81127arXiv0802.2198MaRDI QIDQ970276

Stefan Hollands

Publication date: 17 May 2010

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.2198

zbMATH Keywords

Hochschild cohomologyquantum field theoryquantum algebraoperator product expansion

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) Quantization in field theory; cohomological methods (81T70) Axiomatic quantum field theory; operator algebras (81T05) Operator algebra methods applied to problems in quantum theory (81R15) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45)

Related Items (11)

Associativity of the operator product expansion ⋮ Action principle for OPE ⋮ Covariant star product on semi-conformally flat noncommutative Calabi–Yau manifolds and noncommutative topological index theorem ⋮ The operator product expansion converges in perturbative field theory ⋮ Quantization of spectral curves for meromorphic Higgs bundles through topological recursion ⋮ Vertex Algebras and Renormalization ⋮ Operator product expansion algebra ⋮ Quantum spectral curve for the Gromov-Witten theory of the complex projective line ⋮ Quantum curves for Hitchin fibrations and the Eynard-Orantin theory ⋮ Recursive construction of operator product expansion coefficients ⋮ A universe field theory for JT gravity

This page was built for publication: Axiomatic quantum field theory in terms of operator product expansions: general framework, and perturbation theory via Hochschild cohomology