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A geometrical approach to external potential problems in quantum field theory

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Abstract

A geometrical framework for obtaining the5-operator description of quantum fields interacting with external potentials (including gravitation) is presented. An approach to quantum theory of mutually interacting Bose fields is suggested.

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References

  1. Segal, I. E. (1958).Trans. Am. Math. Soc.,88, 12; (1963).Mathematical Problems in Relativistic Physics, AMS, Providence; (1967). InApplications of Mathematics to Problems in Theoretical Physics, ed. Lurçat, F., Gordon & Breach, New York.

    Article  Google Scholar 

  2. Bogoliubov, N. N. (1947).J. Phys. (USSR),11, 23; Ruijsenaars, S. N. M. (1977).J. Math. Phys.,18, 517.

    Google Scholar 

  3. Shale, D. (1962).Trans. Am. Math. Soc.,103, 149.

    Article  MathSciNet  Google Scholar 

  4. Van Daele, A., and Verbeure, A. (1971).Commun. Math. Phys.,20, 268.

    Article  ADS  Google Scholar 

  5. Seiler, R. (1971). InTroubles in External Field Problem for Invariant Wave Equations, ed. Wightman, A. S., Gordon & Breach, New York.

    Google Scholar 

  6. Bourbaki, N. (1969).Eléments de Mathématique, Livre 6, Chap. 9, Hermann, Paris: Choquet-Bruhat, Y., Dewitt-Morette, C., and Dillard-Bleick, M. (1977).Analysis, Manifolds and Physics, Chap. 7. D, North-Holland, Amsterdam.

    MATH  Google Scholar 

  7. Dewitt, B. S. (1975).Phys. Rep.,19C, No. 6.

  8. Bargmann, V. (1962).Proc. Nat. Acad. Sci.,48, 199; Jauch, J. M. (1968).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.

    Article  ADS  MathSciNet  Google Scholar 

  9. Friedman, J. L., and Schutz, B. F. (1978).Astrophys. J.,221, 937.

    Article  ADS  MathSciNet  Google Scholar 

  10. Chernoff, P. R., and Marsden, J. E. (1974).Properties of infinite dimensional Hamiltonian systems, pp. 211–218, Springer, Berlin.

    Book  MATH  Google Scholar 

  11. Palmer, T. N. (1978).J. Math. Phys.,19, 2324.

    Article  ADS  Google Scholar 

  12. Penrose, R. (1963).Phys. Rev. Lett.,10, 66; (1967).Proc. R. Soc. (London) Ser. A,284, 159.

    Article  ADS  MathSciNet  Google Scholar 

  13. Geroch, R., and Horowitz, G. T. (1978).Phys. Rev. Lett.,40, 203.

    Article  ADS  Google Scholar 

  14. Geroch, R. (1978).J. Math. Phys.,19, 1300.

    Article  ADS  Google Scholar 

  15. Ashtekar, A. (1980).Commun. Math. Phys.,71, 59.

    Article  ADS  MathSciNet  Google Scholar 

  16. Ashtekar, A., and Magnon, A. (1975).Proc. R. Soc. (London) Ser. A,346, 375.

    Article  ADS  Google Scholar 

  17. Magnon-Ashtekar, A. (1976). Thèse d'Etat (revised 1978).

  18. Lichnerowicz, A. (1959).C. R. Acad. Sci. (Paris) 249, 1329, 2287; (1962).Proc. R. Soc. (London) Ser. A,270, 342.

    MathSciNet  Google Scholar 

  19. Ashtekar, A., and Sen, A. (1978). “Quantum fields in curved space-times: Selection and uniqueness of the vacuum,” preprint.

  20. Moreno, C. (1977).J. Math. Phys.,18, 2153; (1978).J. Math. Phys.,19, 92.

    Article  ADS  Google Scholar 

  21. Kay, B. S. (1977). Ph.D. thesis submitted to the University of London; (1979).Commun. Math. Phys.

  22. Penrose, R. (1974). InGroup theory in non-linear problems, ed. Barut, A. O., Reidel, Dordrecht.

    Google Scholar 

  23. Ashtekar, A., and Streubel, M. (1979). “Sympletic geometry of radiation fields and conserved quantities at null infinity,” preprint.

  24. Woodhouse, N. M. J. (1976).Phys. Rev. Lett.,36, 999.

    Article  ADS  MathSciNet  Google Scholar 

  25. Grothendik, A. (1956).Bull. Soc. Math. France,84, 319.

    Article  MathSciNet  Google Scholar 

  26. Glauber, R. J. (1963).Phys. Rev.,130, 2539;131, 2766.

    Article  ADS  MathSciNet  Google Scholar 

  27. Feynman, R. P. (1948).Phys. Rev.,74, 1430.

    Article  ADS  Google Scholar 

  28. Atyah, M. F., and Ward, R. S. (1977).Commun. Math. Phys.,55, 117.

    Article  ADS  Google Scholar 

  29. Penrose, R. (1976).Gen. Rel. Grav.,7, 31.

    Article  ADS  Google Scholar 

  30. Segal, I. E. (1974). InSymposia Mathematica, Vol. 14, p. 99, Academic, New York.

    Google Scholar 

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Authors and Affiliations

  1. Département de Physique, Université de Clermont-Fd., 63170, Aubière, France

    Abhay Ashtekar

  2. Max Planck Institut für Astrophysik, Föhringer Ring 68, München 40, Germany

    Abhay Ashtekar

  3. Département de Mathématiques, Université de Clermont-Fd., 63170, Aubière, France

    Anne Magnon-ashtekar

Authors
  1. Abhay Ashtekar
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  2. Anne Magnon-ashtekar
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Ashtekar, A., Magnon-ashtekar, A. A geometrical approach to external potential problems in quantum field theory. Gen Relat Gravit 12, 205–223 (1980). https://doi.org/10.1007/BF00756233

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