Skip to main content

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 47))

  • 439 Accesses

Abstract

The Cliffordian formalism through the pure spinor theory of Chevalley-Cartan enables one to construct explicitely a torogonal lifting of some reduction of a pseudo-Riemannian structure. Some applications of this construction are given, for instance, in relation with the geometric quantization in Mathematical Physics.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. — Cartan, E. (1938) Leçons sur la théorie des spineurs. Hermann, Paris.

    Google Scholar 

  2. — Chevalley, C. (1954). The algebraic theory of spinors. Columbia University press. New-York.

    MATH  Google Scholar 

  3. — Crumeyrolle, A. (1975). Periodica. Math. Hungarica 6(2).

    Google Scholar 

  4. — Frenkel, J. (1955). Cohomologie à valeurs dans un faisceau non abélien. C.R. Acad. Sci. Paris, 240.

    Google Scholar 

  5. — Greub, W., Petry, H.R. (1978). On the lifting of structure groups II, Proc. Bonn 1977. Springer Lect. Notes in Math. 676.

    Google Scholar 

  6. — Karrer, G. (1973). Darstellung von Clifford Bündeln. Ann. Acad. Sci. Fennicae, serie A, 1, 521.

    Google Scholar 

  7. — Kostant, B. (1970). Quantization and unitary representations. Lect. notes in Math. vol 170. Springer. New-York.

    Google Scholar 

  8. — Souriau, J.M. (1966). Commun. Math. Phys. 1.

    Google Scholar 

  9. — Timbeau, J. a) (1987) Le rôle du concept torogonal dans une préquantification géométrique sur les variétés pseudo-riemanniennes. C.R. Acad. Sci. Paris, t. 305. Série I. b) (1986) Structure torogonale et quantification sur des variétés pseudo-riemanniennes — Thèse — Toulouse c) Twisting procedure on torogonal structures-to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Timbeau, J. (1992). Clifford algebras and torogonal structures. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-8090-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4130-2

  • Online ISBN: 978-94-015-8090-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics