Skip to main content

Eigenvalues of Dirac and Rarita—Schwinger Operators

  • Chapter
  • 1039 Accesses

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

Let M=S 1 × Sn-1 with metric Lorentzian or Riemannian and non-trivial spin structure on S 1, Riemannian metric and standard spin structure on Sn-1, and n even. We give explicit formulas for the eigenvalues of Dirac and Rarita—Schwinger operators on M.

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. T. Branson, Harmonic analysis in vector bundles associated to the rotation and spin groups, J. Funct. Anal. 106, (1992), 314– 328

    Article  MathSciNet  MATH  Google Scholar 

  2. T. Branson, Sharp inequalities, the functional determinant, and the complementary series, Trans. Amer. Math. Soc. 347,(1995), 3671–3742.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Branson, Stein-Weiss operators and ellipticity, J. Funct. Anal. 151, (1997), 334–383

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Branson, Second order conformal covariants, Proc. Amer. Math. Soc. 126, (1998), 1031–1042.

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Branson, Spectra of self-gradients on spheres, J. Lie Theory. 9, (1999), 491–506.

    MathSciNet  MATH  Google Scholar 

  6. T. Branson and O. Hizaji, Bochner-Weitzenbock formulas associated with the Rarita-Schwinger operator. arXiv:hep-th/0110014vl, 1 Oct 2001.

    Google Scholar 

  7. T. Branson, Clifford bundles and Clifford algebras, in Lectures on Clifford Geometric Algebras and Applications, R. Ablamowicz and G. Sobczyk, Eds., Birkhauser, Boston, 2003, Lecture 6, pp. 163–196.

    Google Scholar 

  8. H. Fegan, Conformally invariant first order differential operators, Quart. J. Math. (Oxford) 27, 1976, 371–378.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Lawson and M. Michelsohn, Spin Geometry, Princeton University Press, Princeton, New Jersey, 1989.

    MATH  Google Scholar 

  10. E. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90, (1968), 163–196.

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Warner, Foundations of Differentiate Manifolds and Lie Groups, Scott, Foresman and Company, Glenview, Illinois, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Birkhäuser Boston

About this chapter

Cite this chapter

Hong, D. (2004). Eigenvalues of Dirac and Rarita—Schwinger Operators. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_13

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics