International Journal of Theoretical Physics

, Volume 33, Issue 6, pp 1241–1250 | Cite as

Stochastic quantization of the nonlinear sigma model and the background field method

  • E. Abdalla
  • F. M. de Carvalho Filho
  • Ricardo L. Viana


The background field method is a useful scheme for calculation of the effective action in conventional quantum field theory. In stochastic quantization this approach is introduced by using auxiliary fields, as suggested by Okano. In this work, we implement the background field method, using the normal coordinate expansion, for the nonlinear sigma model on a general Riemannian manifold in the context of stochastic quantization. We also calculate, making use of this novel formulation, the action necessary for investigation of the divergences, at least at the one-loop level.


Manifold Field Theory Elementary Particle Quantum Field Theory Riemannian Manifold 
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  1. Abbott, L. F. (1981).Nuclear Physics B,185, 189.Google Scholar
  2. Abdalla, E., and Viana, R. L. (1989).Modern Physics Letters A,4, 491.Google Scholar
  3. Alvarez-Gaumé, L., Freedman, D. Z., and Mukhi, S. (1981).Annals of Physics,134, 85.Google Scholar
  4. Brunelli, J. C., and Gomes, M. (1992).Physical Review D,46, 2617.Google Scholar
  5. Chaturvedi, S., Kapoor, A. K., and Srinivasan, V. (1986).Physical Review D,34, 3846.Google Scholar
  6. Damgaard, P. H., and Hüffel, H. (1987).Physics Reports,152, 227.Google Scholar
  7. DeWitt, B. S. (1967).Physical Review,162, 1195.Google Scholar
  8. Honerkamp, J. (1972).Nuclear Physics B,36, 130.Google Scholar
  9. Namiki, M., and Yamanaka, Y. (1986).Progress of Theoretical Physics,75, 1447.Google Scholar
  10. Okano, K. (1987).Nuclear Physics B,289, 109.Google Scholar
  11. Parisi, G., and Wu, Y.-S. (1981).Scientia Sinica,24, 483.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. Abdalla
    • 1
  • F. M. de Carvalho Filho
    • 2
  • Ricardo L. Viana
    • 3
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  2. 2.Escola Federal de Engenharia de ItajubáItajubá, Minas GeraisBrazil
  3. 3.Departamento de FísicaUniversidade Federal do ParanáCuritiba, 81531-970, ParanáBrazil

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