<script type="text/javascript">
<!--
document.write('<div id="oa_widget"></div>');
document.write('<script type="text/javascript" src="https://www.openaire.eu/index.php?option=com_openaire&view=widget&format=raw&projectId=undefined&type=result"></script>');
-->
</script>

COPY SCRIPT

For further information contact us at helpdesk@openaire.eu

Geometry of differential operators and odd Laplace operators

Geometry of differential operators, and odd Laplace operators.

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 28 Feb 2003Embargo end date: 01 Jan 2003Publisher:Steklov Mathematical InstituteJournal:Russian Mathematical Surveys, volume 58, pages 197-198 (issn: 0036-0279, eissn: 1468-4829,

Authors: Theodore Voronov; H. M. Khudaverdian;

doi: 10.1070/rm2003v058n01abeh000597 , 10.48550/arxiv.math/0301236

arXiv: http://arxiv.org/abs/math/0301236

Geometry of differential operators and odd Laplace operators

- Summary
- Subjects
- Metrics

Abstract

We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary weights appear naturally in the course of study. We show that for the algebra of densities it is possible to establish a one-to-one correspondence between operators and brackets generated by them. Everything is applicable to supermanifolds as well as to usual manifolds. In the super case the problem is closely connected with the geometry of the Batalin--Vilkovisky formalism in quantum field theory, namely the description of the generating operators for an odd bracket. We give a complete answer. This text is a concise outline of the main results. A detailed exposition is in \texttt{arXiv:math.DG/0212311}.

LaTeX2e; 3 pages; Russian and English versions available

Keywords

Mathematics - Differential Geometry, High Energy Physics - Theory, Elliptic equations on manifolds, general theory, connection, FOS: Physical sciences, Mathematical Physics (math-ph), Laplace operator, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Mathematics - Symplectic Geometry, supermanifold, FOS: Mathematics, Symplectic Geometry (math.SG), Analysis on supermanifolds or graded manifolds, bracket, Mathematical Physics

Impact byBIP!

	citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	3
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

Average

Green

bronze

Fields of Science

Fields of Science