International Journal of Theoretical Physics

, Volume 45, Issue 12, pp 2396–2406 | Cite as

BRST Invariant Theory of a Generalized 1 + 1 Dimensional Nonlinear Sigma Model with Topological Term

  • Yong-Chang Huang
  • Kai-Hua Yang
  • Xi-Guo Lee


We give a generalized Lagrangian density of 1 + 1 Dimensional O(3) nonlinear σ model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear σ model, give the example of not introducing the lost constraint \(\dot N\) = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter β originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.


σ model gauge condition BRST transformation commutative relation constraint system 


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  1. Coleman, S., Weiss, J., and Zumino, B. (1961). Physical Revew 177, 2239; Callan, C., Coleman, S., Weiss, J., and Zumino, B. (1969). Physical Revew 177, 2247.Google Scholar
  2. Vainshtein, A. I., Zakharov, V. I., Novikov, V. A., and Shifman, M. A. (1986). Sov. J. Pant, Nucl., 17, 204; Zamolodchikov, A. B. (1979). Annals Physics (NY), 120, 253.Google Scholar
  3. Li, M. and Wu, Y. S. (2000). Physical Review Letters, 84, 2084.MATHMathSciNetCrossRefADSGoogle Scholar
  4. Polyakov, A. M. (1975). Physics Letters B 59, 79; Novikv, V. A., et al. (1984). Physical Repots 116, 103.Google Scholar
  5. Wilczek, F., and Zee, A. (1983). Physical Review Letters 51, 2250; Bowick, M. J., Karabali, D., Wijewardhana, L. C. R. (1986). Nuclear Physics B 271, 417; and references therein.Google Scholar
  6. Wu, Y. S., Zee, A. (1984). Physical Letteers 147B, 325; Panigrahi, P., Roy, S., and Scherer, W. (1988). Physical Review D 38, 3199; Physical Review Letteres 61, 2827.Google Scholar
  7. Polyakov, A. M. (1988). Modern Physics Letters A3, 455; Dzyaloshinskii, I., Polyakov, A. M., and Wiegmann, P. (1988). Physics Letters A 127, 112.Google Scholar
  8. Wiegmann, P. B. (1988). Physical Review Letters 60, 821.CrossRefADSGoogle Scholar
  9. Itoh, T., Oh, P., and Ryou, C. (2001). Physical Review D 64, 045005/1-5.Google Scholar
  10. Yurkevich, I. V. and Lerner, I. V. (2001). Physical Review B 64, 054515/1-5.Google Scholar
  11. Kamenev, A. (2000). Physical Review Letters 85(19), 4160.CrossRefADSGoogle Scholar
  12. Becchi, C., Rouet, A., and Stora, R. (1975/1976). Communication in Mathematical Physics 42, 127; Annual Physics 98, 287.Google Scholar
  13. t’Hooft, G. (1971). Nuclear Physics B 33, 173; Nuclear Physics B 35, 167; t’Hooft, G. and Veltman, M. (1972). Nuclear Physics B 44, 189; Lee, B. W. and Zinn-Justin, J. (1972/1973). Physical Review D 5, 3121; D 7, 1049; Lee, B.W. (1974). Physical Review D 9, 938.Google Scholar
  14. Kugo, T. and Ojima, I. (1979). Progress of Theoretical Physics Suppliment 66, 1.MathSciNetADSGoogle Scholar
  15. Fradkin, E. S. and Vilkovisky, G. A. (1975). Physics Letters B 55, 224; Batalin, I. A. and Vilkovisky, G. A. (1977). Physics Letters B 69, 309.Google Scholar
  16. Kato, M. and Ogawa, K. (1983). Nuclear Physics B 212, 443; Hwang, S. (1983). Physical Review D 28, 2614; Siegel, W. (1984). Physics Letters B 149, 157, 162.Google Scholar
  17. Dirac, P. A. M. (1964). Lectures in Quantum Mechanics, Yeshiva University, New York.Google Scholar
  18. Banerjee, R. (1993). Physical Review D 48, R5467; Kim, W. T. and Park, Y.-J. (1994). Physics Letters B 336, 376; Henneaux, M. and Wilch, A. (1998) Physical Review D 58, 025017.Google Scholar
  19. Kim, Y.-W., Park, Y.-J., and Rothe, K. D. (1998). Journal of Physics G 24, 953; Kim, Y.-W. and Rothe, K. D. (1998). Nuclear Physics B 510, 511; Ghosh, S. (1994). Physical Review D 49, 2990; Amorim, R. and Barcelos-Neto, J. (1996). Physical Review D 53, 7129; Nativiade, C. P. and Boschi-Filho, H. (2000). Physical Review D 62, 025016.Google Scholar
  20. Banerjee, N., Ghosh, S., and Banerjee, R. (1994). Physical Review D 49, 1996.MathSciNetCrossRefADSGoogle Scholar
  21. Banerjee, R. (1994). Physical Review D 49, 2133.MathSciNetCrossRefADSGoogle Scholar
  22. Henneaux, M. and Teitelboim, C. (1992). Quantization of Gauge Systems, Princeton University Press, Princeton, New Jersey.MATHGoogle Scholar
  23. Gitman, D. M. and Tyutin, I. V. (1990). Quantization of Fields with Constraints, Springer-Verlag, Berlin.MATHGoogle Scholar
  24. Voruganti, P. (1989). Physical Review D 39, 1179.MathSciNetCrossRefADSGoogle Scholar
  25. Itzykson, C., Zuber, J.-B. (1980). Quantum Field Theory, Mcgraw-Hill International Book Company, New York.Google Scholar
  26. Huang, Y. C., Ma, F. C., and Zhang, N. (2004). Modern Physics Letterrs B 18, 1367.MathSciNetCrossRefADSGoogle Scholar
  27. Huang, Y. C. and Weng, G. (2005). Communication in Theoretical Physics 44, 757.CrossRefGoogle Scholar
  28. Huang, Y. C., Lee, X. G., and Shao, M. X. (2006). Modern Physics Letters A 21, 1107.CrossRefADSMATHGoogle Scholar
  29. Huang, Y. C. and Lin, B. L. (2002). Physics Letters A 299, 6449.MathSciNetGoogle Scholar
  30. Friedan, D. (1980). Physical Review Letters 45, 1057.MathSciNetCrossRefADSGoogle Scholar
  31. Friedan, D. H. (1985). Annual Physics 163, 318.MATHMathSciNetCrossRefADSGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Yong-Chang Huang
    • 1
    • 3
    • 4
    • 5
  • Kai-Hua Yang
    • 1
  • Xi-Guo Lee
    • 2
    • 4
  1. 1.Institute of Theoretical Physics, College of Applied Mathematics and PhysicsBeijing University of TechnologyBeijingP. R. China
  2. 2.Institute of Modern PhysicsChinese Academy of SciencesLanzhouP.R. China
  3. 3.CCAST (World Lab.)BeijingP. R. China
  4. 4.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy Ion CollisionsLanzhouP.R. China
  5. 5.Institute of Theoretical Physics, College of Applied SciencesBeijing University of TechnologyBeijingP.R. China

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