Odd Scalar Curvature in Field-Antifield Formalism

BATALIN, Igor and Klaus BERING LARSEN. Odd Scalar Curvature in Field-Antifield Formalism. Journal of Mathematical Physics. USA: American Institute of Physics, 2008, vol. 2008, 49 033515, p. 1-22. ISSN 0022-2488. Available from: https://dx.doi.org/10.1063/1.2835485.

Basic information

• Original name: Odd Scalar Curvature in Field-Antifield Formalism
• Name in Czech: Odd Scalar Curvature in Field-Antifield Formalism
• Authors: BATALIN, Igor (643 Russian Federation) and Klaus BERING LARSEN (208 Denmark, guarantor, belonging to the institution).
• Edition: Journal of Mathematical Physics, USA, American Institute of Physics, 2008, 0022-2488.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10303 Particles and field physics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.085
• RIV identification code: RIV/00216224:14310/08:00025619
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1063/1.2835485
• UT WoS: 000254537500044
• Keywords in English: BV Field-Antifield Formalism; Odd Laplacian; Antisymplectic Geometry; Semidensity; Antisymplectic Connection; Odd Scalar Curvature.
• Tags: Antisymplectic Connection, Antisymplectic Geometry, BV Field-Antifield Formalism, Odd Laplacian, Odd Scalar Curvature., Semidensity
• Tags: International impact, Reviewed

Abstract

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function \nu is not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density \rho. The main impact of introducing the \nu term is that it makes compatibility relations between E and \rho obsolete. We give a geometric interpretation of \nu as (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and Ricci-form-flat connection. Finally, we speculate on how the density \rho could be generalized to a non-flat line bundle connection.

Abstract (in Czech)

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function \nu is not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density \rho. The main impact of introducing the \nu term is that it makes compatibility relations between E and \rho obsolete. We give a geometric interpretation of \nu as (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and Ricci-form-flat connection. Finally, we speculate on how the density \rho could be generalized to a non-flat line bundle connection.

Links

• MSM0021622409, plan (intention): Name: Matematické struktury a jejich fyzikální aplikace

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications