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Higher Spin Fields on Smooth Domains

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Clifford Analysis and Its Applications

Part of the book series: NATO Science Series ((NAII,volume 25))

Abstract

This paper deals with a generalization of the classical Rarita-Schwinger equations for spin 3/2-fields to the case of functions taking values in irreducible representation spaces with weight k + 1/2 (realised as functions taking values in spaces of spherical monogenics earlier considered in [SVA2]). In this paper we consider such fields on smooth domains in ℝm.

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References

  1. F. Brackx, R. Delanghe and F. Sommen: Clifford Analysis, Pitman, London, 1982.

    MATH  Google Scholar 

  2. J. Bures, F. Sommen, V. Soucek, P. Van Lancker: Rarita-Schwinger operators in Clifford Analysis, Preprint.

    Google Scholar 

  3. J. Bures, P. Van Lancker, F. Sommen, V. Souček: Symmetric analogues of Rarita-Schwing er equations, Preprint.

    Google Scholar 

  4. D. M. J. Calderbank: Clifford analysis for Dirac operators on manifolds with boundary, Report MPI 96–131.

    Google Scholar 

  5. R. Delanghe, F. Sommen, V. Soucek: Clifford analysis and spinor valued functions, Kluwer Acad. Publ., Dordrecht, 1992.

    Book  Google Scholar 

  6. J. Gilbert and M. Murray: Clifford algebras and Dirac operators in harmonic analysis, Cambridge University Press, 1991.

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  7. N. Kerzman, E. M. Stein: The Cauchy kernel, the Szegö kernel, and the Riemann mapping function, Math. Ann. 236, 1978, pp. 85–93.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Sommen: Clifford analysis in two and several vector variables, Appl. Anal. Vol. 73(1-2), pp. 225–253.

    Google Scholar 

  9. V. Soucek: Higher Spins and Conformal Invariance in Clifford Analysis, Proc. Conf. Seiffen, 1996.

    Google Scholar 

  10. F. Sommen, N. Van Acker: Monogenic Differential Operators, Results in Math. 22, 1992, pp. 781–798.

    MATH  Google Scholar 

  11. F. Sommen, N. Van Acker: Invariant differential operators on polynomial valued functions, F. Brackx et al. (eds.), Clifford Algebras and their Applications in Mathematical Physics, Kluwer Acad. Publ., 1993, pp. 203–212.

    Google Scholar 

  12. P. Van Lancker: Clifford Analysis on the Unit Sphere, Ph. D. thesis, University of Gent, 1996.

    Google Scholar 

  13. P. Van Lancker: The Kerzman-Stein Theorem on the Sphere, to appear in Complex Variables.

    Google Scholar 

  14. P. Van Lancker, F. Sommen, D. Constales: Models for irreducible representations of Spin(m), to appear in the Proc. of Conf. on Dirac Operators, Cetraro, 1998.

    Google Scholar 

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© 2001 Springer Science+Business Media Dordrecht

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Van Lancker, P. (2001). Higher Spin Fields on Smooth Domains. In: Brackx, F., Chisholm, J.S.R., Souček, V. (eds) Clifford Analysis and Its Applications. NATO Science Series, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0862-4_33

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  • DOI: https://doi.org/10.1007/978-94-010-0862-4_33

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7045-1

  • Online ISBN: 978-94-010-0862-4

  • eBook Packages: Springer Book Archive

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