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Differential Geometrical Methods in Mathematical Physics II pp 513–534Cite as

On functional integrals in curved spacetime

  • Chapter III. Quantum Field Theory And General Relativity
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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 676))

Abstract

We discuss the functional integral formulation of curved space quantum field theory for fields of spin 0, 1/2 and 1. We give a discussion of the Ghost problem and demonstrate gauge invariance of the formalism. We discuss the significance of the zero frequency modes, their relation to Black Hole, No Hair Theorems, and to the Topology of the space one works on. We use the formalism to evaluate the zero point energy of quantum fields in a static enclosure and the electromagnetic trace anomaly.

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References

  1. S.W. Hawking, Commun. Math. Phys. 55, 133 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  2. G.W. Gibbons, S.W. Hawking and M.J. Perry, in preparation.

    Google Scholar 

  3. R.T. Seeley, Amer. Math. Soc. Proc. Symp. Pure Math. 10, 288–307 (1976)

    Article  Google Scholar 

  4. P. Gilkey, Journ. Diff. Geom. 10, 601 (1975)

    MathSciNet  MATH  Google Scholar 

  5. S.W. Hawking, Phys. Letts. A60, 81 (1977)

    Article  MathSciNet  Google Scholar 

  6. N. Hitchin, Journ. Diff. Geom. 9, 435 (1974)

    MathSciNet  MATH  Google Scholar 

  7. H.S. Tsao, Phys. Letts. 68B, 79 (1977)

    Google Scholar 

  8. J.S. Dowker and R. Critchley, "The Stress Tensor Conformal Anomaly of Scalar and Spinor Fields", Manchester preprint to appear in Phys. Rev. D 15

    Google Scholar 

  9. L.S. Brown and J.P. Cassidy, Phys. Rev. D 15, 2810 (1977)

    Article  Google Scholar 

  10. D.M. Capper and M.J. Duff, Nuovo Cimento 23A, 175 (1974)

    Google Scholar 

  11. G.W. Gibbons, Phys. Letts. 60A, 385 (1977)

    Article  Google Scholar 

  12. L.M. Ford, Phys. Rev. D 11, 3370 (1975)

    Article  Google Scholar 

  13. L.M. Ford, Phys. Rev. D 14, 3304–3314 (1976)

    Article  Google Scholar 

  14. J.S. Dowker and Critchley, J. Phys. A9, 535 (1976) Phys. Rev. D 15, 1484 (1976)

    MathSciNet  Google Scholar 

  15. J.S. Dowker and M.B. Altaie, "Spinor Fields in an Einstein Universe. The vacuum averaged stress-energy tensor", Manchester preprint

    Google Scholar 

  16. S. Minakshisundaram, Journ. Ind. Math. Soc. 13, 41 (1949)

    MathSciNet  MATH  Google Scholar 

  17. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2752 (1977)

    Article  MathSciNet  Google Scholar 

  18. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2738 (1977)

    Article  MathSciNet  Google Scholar 

  19. B. Carter in "Black Holes" B.S. Witt and C. de Witt ed. Gorden and Breach, London (1973)

    Google Scholar 

  20. L.T. Eguchi and P. Freund, Phys. Rev. Letts. 37, 1251 (1976)

    Article  MathSciNet  Google Scholar 

  21. S.T. Yau, Proc. Natl. Acad. Sci. USA 74, 1798 (1977)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Physik und Astrophysik, Föhringer Ring 6, 8000, München 40, W-Germany

    G. W. Gibbons

  2. Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge

    G. W. Gibbons

Authors
  1. G. W. Gibbons
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Editor information

Konrad Bleuler Axel Reetz Herbert Rainer Petry

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© 1978 Springer-Verlag

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Gibbons, G.W. (1978). On functional integrals in curved spacetime. In: Bleuler, K., Reetz, A., Petry, H.R. (eds) Differential Geometrical Methods in Mathematical Physics II. Lecture Notes in Mathematics, vol 676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063687

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  • DOI: https://doi.org/10.1007/BFb0063687

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08935-3

  • Online ISBN: 978-3-540-35721-6

  • eBook Packages: Springer Book Archive

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