Skip to main content

The Circle as a Fermionic Distribution

  • Conference paper

Part of the book series: Progress in Probability ((PRPR,volume 38))

Abstract

Let us consider the free loop space of a manifold. It is very well known that the equivariant cohomology of the free loop spce is related to the index theorem for a finite dimensional Dirac operator. The reader can see [Bis85], [Bis86], [GJP90], [JP90] for instance.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. M. Bismut. Large deviations and the Malliavin calculus Progress in Math. 45. Birkhaüser, 1984.

    Google Scholar 

  2. J. M. Bismut. Index theorems and equivariant cohomology of the loop space. C. M. P., 98: 213–237, 1985.

    MATH  MathSciNet  Google Scholar 

  3. J. M. Bismut. Localisation formula, superconnections and the index theorem for families. C. M. P., 103: 127–166, 1986.

    MATH  MathSciNet  Google Scholar 

  4. E. Getzler, J. D. S. Jones, and S. Petrack. differential forms on a loop space and the cyclic bar complex. Topology, 30: 339–373, 1990.

    Article  MathSciNet  Google Scholar 

  5. R. Hoegh-Krohn. Relativistic quantum mechanics in 2 dimensional space time. C. M. P., 38: 195–224, 1974.

    MathSciNet  Google Scholar 

  6. T. Hida, H.H. Kuo, J. Potthoff, and L. Streit. White noise: an infinite dimensional calculus. Kluwer, 1993.

    MATH  Google Scholar 

  7. J. D. S. Jones and R. Leandre. A stochastic approach to the Dirac operator over free loop spaces. In preparation.

    Google Scholar 

  8. J. D. S. Jones and R. Leandre. l p chen forms over loop spaces. In Stochastic Analysis, pages 104–162. Cambridge University Press, 1991.

    Google Scholar 

  9. J. Jones and S. Petrack. The pinced point theorems in equivariant cohomology. Trans. Amer. Math. Soci., 1: 35–49, 1990.

    Article  MathSciNet  Google Scholar 

  10. R. Leandre. Brownian cohomology of an homogeneous manifold. In preparation.

    Google Scholar 

  11. R. Leandre. Brownian motion over a KHahler manifold and elliptic genera of level N. To be published in the proceedings of the conference probability and physic, ed. Streit, L.

    Google Scholar 

  12. R. Leandre. Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entière. Preprint.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Birkhäuser Boston

About this paper

Cite this paper

Leandre, R. (1996). The Circle as a Fermionic Distribution. In: Körezlioğlu, H., Øksendal, B., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics V. Progress in Probability, vol 38. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2450-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2450-1_11

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7541-1

  • Online ISBN: 978-1-4612-2450-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics