{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1360574093813617664.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1142/s0217751x97001031"}},{"identifier":{"@type":"URI","@value":"https://www.worldscientific.com/doi/pdf/10.1142/S0217751X97001031"}}],"dc:title":[{"@value":"The Geometry of the Master Equation and Topological Quantum Field Theory"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:p> In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some construction of QP-manifolds and prove a classification theorem (under certain conditions). </jats:p><jats:p> We apply these geometric constructions to obtain in a natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern–Simons theory in BV-formalism arises as a sigma-model with target space [Formula: see text]. (Here [Formula: see text] stands for a Lie algebra and Π denotes parity inversion.) </jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380025430172870666","@type":"Researcher","foaf:name":[{"@value":"M. Alexandrov"}],"jpcoar:affiliationName":[{"@value":"University of California at Davis, Department of Mathematics, Davis, CA 95616, USA"}]},{"@id":"https://cir.nii.ac.jp/crid/1380574093813617664","@type":"Researcher","foaf:name":[{"@value":"A. Schwarz"}],"jpcoar:affiliationName":[{"@value":"University of California at Davis, Department of Mathematics, Davis, CA 95616, USA"}]},{"@id":"https://cir.nii.ac.jp/crid/1380574093813617667","@type":"Researcher","foaf:name":[{"@value":"O. Zaboronsky"}],"jpcoar:affiliationName":[{"@value":"University of California at Davis, Department of Mathematics, Davis, CA 95616, USA"}]},{"@id":"https://cir.nii.ac.jp/crid/1380574093813617665","@type":"Researcher","foaf:name":[{"@value":"M. Kontsevich"}],"jpcoar:affiliationName":[{"@value":"University of California at Berkeley, Department of Mathematics, Berkeley, CA 94720, USA"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"0217751X"},{"@type":"EISSN","@value":"1793656X"}],"prism:publicationName":[{"@value":"International Journal of Modern Physics A"}],"dc:publisher":[{"@value":"World Scientific Pub Co Pte Lt"}],"prism:publicationDate":"1997-03-20","prism:volume":"12","prism:number":"07","prism:startingPage":"1405","prism:endingPage":"1429"},"reviewed":"false","url":[{"@id":"https://www.worldscientific.com/doi/pdf/10.1142/S0217751X97001031"}],"createdAt":"2003-10-20","modifiedAt":"2019-08-07","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360009142497203840","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Global aspects of doubled geometry and pre-rackoid"}]},{"@id":"https://cir.nii.ac.jp/crid/1360022306714779008","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Differential Graded Manifolds of Finite Positive Amplitude"}]},{"@id":"https://cir.nii.ac.jp/crid/1360025430172870656","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Geometric BV for twisted Courant sigma models and the BRST power finesse"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298754834833664","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The BV action of 3D twisted R-Poisson sigma models"}]},{"@id":"https://cir.nii.ac.jp/crid/1360306904389758464","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Current algebras from QP-manifolds in general dimensions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576118828411648","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Higher Dimensional Lie Algebroid Sigma Model with WZ Term"}]},{"@id":"https://cir.nii.ac.jp/crid/1360587972817843456","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Equivariant BV-BFV formalism"}]},{"@id":"https://cir.nii.ac.jp/crid/1360587973827554944","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"A topological quantum field theory for Spin(7)-instantons"}]},{"@id":"https://cir.nii.ac.jp/crid/1360589285733573888","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"The Atiyah class of DG manifolds of amplitude +1"}]},{"@id":"https://cir.nii.ac.jp/crid/1390573242737844480","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Quantum Computing: The Future of Big Data and Artificial Intelligence in Spine"}]},{"@id":"https://cir.nii.ac.jp/crid/2050588892108564736","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Perturbative path-integral of string fields and the A∞ structure of the BV master equation"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1142/s0217751x97001031"},{"@type":"CROSSREF","@value":"10.1063/5.0020127_references_DOI_3HDL70ZSdA2f6IA1kgkE5Yvb6lh"},{"@type":"CROSSREF","@value":"10.1093/imrn/rnae023_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1007/jhep07(2024)115_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1007/jhep10(2022)002_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1093/ptep/ptac132_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1063/5.0186227_references_DOI_3HDL70ZSdA2f6IA1kgkE5Yvb6lh"},{"@type":"CROSSREF","@value":"10.3390/universe7100391_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1016/j.geomphys.2025.105684_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1016/j.geomphys.2025.105630_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.1016/j.geomphys.2026.105774_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"},{"@type":"CROSSREF","@value":"10.22603/ssrr.2021-0251_references_DOI_GXrdNl8ozjh4SCbOhxFDCHLWu7b"}]}