Fermionic Integration

Victor W. Guillemin, Shlomo Sternberg and Jochen Brüning
Additional contact information
Victor W. Guillemin: Massachusetts Institute of Technology, Department of Mathematics
Shlomo Sternberg: Harvard University, Department of Mathematics
Jochen Brüning: Humboldt-Universität Berlin, Institut für Mathematik Mathematisch-Naturwissenschaftliche Fakultät II

Chapter Chapter 7 in Supersymmetry and Equivariant de Rham Theory, 1999, pp 77-93 from Springer

Abstract: Abstract Fermionic integration was introduced by Berezin [Be] and is part of the standard repertoire of elementary particle physicists. It is not all that familiar to mathematicians. However it was used by Mathai and Quillen [MQ] in their path breaking paper constructing a “universal Thom form”. In this chapter we will develop enough of Berezin’s formalism to reproduce the MathaiQuillen result. We will also discuss the Fermionic Fourier transform and combine Bosonic and Fermionic Fourier transforms into a single “super” Fourier transform. We will see that there is an equivariant analogue of compactly supported cohomology which can be obtained from the Koszul complex by using this super Fourier transform, and use this to explain the Mathai-Quillen formula. In Chapter 10 we will apply these results to obtain localization theorems in equivariant cohomology.

Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-03992-2_7

Ordering information: This item can be ordered from
http://www.springer.com/9783662039922

DOI: 10.1007/978-3-662-03992-2_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().