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Spin Structures on Hypersurfaces and the Spectrum of the Dirac Operator on Spheres

  • Andrzej Trautman
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 52)

Abstract

Recent results on pin structures on hypersurfaces in spin manifolds are reviewed. A new form of the Dirac operator is used to compute its spectrum on n-dimensional spheres. This constrbution is based on two papers by the author, where details and proofs can be found (Ref.4 and 5).

Keywords

Dirac Operator Clifford Algebra Killing Spinor Spinor Field Spin Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M.F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology, 3 Suppl. 1(1964)3–38MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. Trautman, The Dirac operator on hypersurfaces in Euclidean space, Trieste Seminar on Spinors, Letter 13 (10 April 1991).Google Scholar
  3. [3]
    S. Gutt, Killing spinors on spheres and projective spaces, in: “Spinors in Physics and Geometry” (Proc. Conf. Trieste, 11-13 Sept. 1986) ed. by A. Trautman and G. Furlan, World Scientific, Singapore, 1988.Google Scholar
  4. [4]
    A.Trautman, Spinors and the Dirac operator on hypersurfaces. I. General Theory, J.Math.Phys. (in print).Google Scholar
  5. [5]
    A.Trautman and E. Winkowska, Spinors and the Dirac operator on hypersurfaces.II. The spheres as an example (in preparation).Google Scholar
  6. [6]
    S.Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol.1, Interscience, New York, 1963.MATHGoogle Scholar
  7. [7]
    L. Dabrowski and A.Trautman, Spinor structures on spheres and projective spaces, J.Math.Phys. 27(1986)2022–2028.MathSciNetADSMATHCrossRefGoogle Scholar
  8. [8]
    A.Lichnerowicz, Spineurs harmoniques, C.R. Acad.Sei.Paris A-B 257(1963)7–9.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Andrzej Trautman
    • 1
  1. 1.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland

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