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Gauge coupling of non-linear σ-model and a generalized Mazur identity

  • B. Carter
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 226)

Abstract

An inversionsymmetric class of non-linear σ-models is constructed. The original pure model with field values in the coset space of a classical matrix group G with respect to an isotropy subgroup under the adjoint action is generalized to a minimally gauge coupled model in which the field is a section in a bundle with group G acting on the coset space as fibre with a nontrivial connection of (for example) Yang-Mills type. It is shown that the gauge coupled models admit a natural generalisation of the identities originally constructed by Mazur for the pure nonlinear σ-models whereby the divergence of a quantity whose surface integral vanishes when suitable boundary conditions are satisfied is shown to be equal to a functional of the difference between two sets of field variables that is positive definite in many relevant situation. In such cases, which occur when the base-space metric is positive definite (so that the system is of elliptic type) and the isotropy subgroup is compact, the identities lead directly to uniqueness theorems for the solutions.

Keywords

Base Space Adjoint Action Isotropy Subgroup Coset Space Suitable Boundary Condition 
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References

  1. (1).
    R. Geroch (1971) J. Math. Phys. 12, 918.CrossRefGoogle Scholar
  2. (2).
    W. Kinnersley (1973) J. Math. Phys. 14, 651.CrossRefGoogle Scholar
  3. (3).
    N. Sanchez (1982) Phys. Rev. D26, 2589.Google Scholar
  4. (4).
    P.O. Mazur (1983) Acta Physica Polonica, B14, 219.Google Scholar
  5. (5).
    P.O. Mazur (1982) J. Phys. A15, 3173.Google Scholar
  6. (6).
    B. Carter (1971) Phys. Rev. Lett., 26, 331.CrossRefGoogle Scholar
  7. (7).
    D.C. Robinson (1974) Phys. Rev. D10, 458.Google Scholar
  8. (8).
    D.C. Robinson (1975) Phys. Lett. 34, 905.CrossRefGoogle Scholar
  9. (9).
    B. Carter (1973) in Black Holes ed. B. and C. Dewitt, Gordon and Breach, New York.Google Scholar
  10. (10).
    B. Carter (1979) in General Relativity ed. S. W. Hawking and W. Israel, Cambridge U.P..Google Scholar
  11. (11).
    G. Bunting (1981) The Black Hole Uniqueness Theorem in unpublished proceedings of the 2nd Australian Mathematics Convention Sydney, 11–15 May, 1981.Google Scholar
  12. (12).
    G. Bunting (1983) Proof of the Uniqueness Conjecture for Black Holes, Ph.D. Thesis, Dept of Mathematics, University of New England, Armidale, N.S.W..Google Scholar
  13. (13).
    B. Carter (1984) preprint, Observatoire de Paris-Meudon.Google Scholar
  14. (14).
    B. Carter (1979) in Recent Developments in Gravitation (Cargèse, 1978), in Nato Advanced Study Institutes, Series B44, ed. M. Levy and S. Deser Plenum, New YorkGoogle Scholar
  15. (14a).
    M. Levy and S. Deser Plenum, New York.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • B. Carter
    • 1
  1. 1.Groupe d'Astrophysique Relativiste D.A.F.Observatoire de Paris-MeudonFrance

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