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Chinese Physics C> 2002, Vol. 26> Issue(2) : 122-128 

Generalized Ward Identities for Non-local Transformation

  •  College of Applied Science, Beijing Polytechnic University, Beijing 100022, China

  • Based on the phase-space generating functional of Green function for a system with a singular higher-order Lagrangian, the generalized canonical Ward identities under the local and non-local transformation in phase space for such a system have been derived. Starting from the configuration-space generating functional for a gauge-invariant system, the generalized Ward identities were deduced under the local, non-local and global transformation, respectively. The applications to the non-Abelian Chern-Simons theories with higher derivatives were given. Some relationships among the proper vertices have been deduced, in which one does not need to carry out the integration over canonical momenta in phase-space generating functional. The Ward-Takahashi identities for BRS transformation are also obtained.
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    [1] . LI Z P. Science in China(Scientia Sinica), Series A, 1993, 36: 1212; Phys. Rev., 1994, E50: 8762. Foussats A, Manavella E, Repetto C etal. Int. J. Theor. Phys., 1995, 34: 1037; J. Math. Phys., 1996, 37: 84 3. Mizrahi M M. J Math. Phys., 1978, 19: 2984. LI Z P. Int. J. Theor. Phys., 1995, 34: 523; 1999, 38: 1677 5. Gitman D M, Tyutin I V, Quantization of Fields with Constraints, Springer Verlag, Berlin, 1990 6. LI Z P, JIANG J H. Symmetries in Constrained Canonical System, Science Press, Beijing, 20007. LI Z P. Int. J. Theor. Phys., 1995, 34: 19458. LI Z P, BAO J. Europhys. Lett., 1997, 39: 599 9. Deser S, Jackiw R, Templeton S. Ann. Phys., 1982, 140: 372

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LI Zi-Ping and LI Rui-Jie. Generalized Ward Identities for Non-local Transformation[J]. Chinese Physics C, 2002, 26(2): 122-128.
LI Zi-Ping and LI Rui-Jie. Generalized Ward Identities for Non-local Transformation[J]. Chinese Physics C, 2002, 26(2): 122-128. shu
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Received: 2001-04-16
Revised: 1900-01-01
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Generalized Ward Identities for Non-local Transformation

    Corresponding author: LI Zi-Ping,
  • College of Applied Science, Beijing Polytechnic University, Beijing 100022, China
  • Received Date: 2001-04-16
  • Accepted Date: 1900-01-01
  • Available Online: 2002-02-05

Abstract: Based on the phase-space generating functional of Green function for a system with a singular higher-order Lagrangian, the generalized canonical Ward identities under the local and non-local transformation in phase space for such a system have been derived. Starting from the configuration-space generating functional for a gauge-invariant system, the generalized Ward identities were deduced under the local, non-local and global transformation, respectively. The applications to the non-Abelian Chern-Simons theories with higher derivatives were given. Some relationships among the proper vertices have been deduced, in which one does not need to carry out the integration over canonical momenta in phase-space generating functional. The Ward-Takahashi identities for BRS transformation are also obtained.

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