Noether Identities at the Quantum Level

  • Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived. For the gauge-invariant system, the quantal Noether identities in configuration space have been also deduced. It is pointed out that in certain cases the quantal Noether identities may be converted to quantal conservation laws of the system. This method for obtaining the quantal conservation laws is significantly different from the first Noether theorem at the quantum level. The application to non-Abelian CS theories is studied, the quantal conserved BRS and PBRS charges are obtained, and these two conserved charges are totally different.
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  • [1] LI Z P. Classical and Quanta1 Dynamics of Constrained System and Their Symmetry Properties, Beijing, Beijing Polytechnic University Press, 1993(in Chinese)(李子平. 经典和量子约束系统及其对称性质, 北京: 北京工业大学出版社, 1993)2 LI Z P. Int. J. Theor. Phys., 1995.34: 19453 LI Z P. Science in China (Scientia Sinica) , Series A, 1993,36: 12124 LI Z P. Phys. Rev., 1994, E50:8765 LI Z P. Int . J. Theor. PhYS., 1994,33: 12076 LI Z P. Science in China ( Scientia Sinica), Series A. 1996, 39: 7397 LI Z P. Z. Phys., 1997, C76: 1818 Mizrahi M M. J. Math. Phys., 1978, 19: 2989 LI Z P. Int. J. Theor. Phys., 1995, 34: 52310 LI Z P. lnt. J. Theor. Phys., 1987, 26: 85311 Young B L, Introduction to Quantum Field Theories. Beijing, Science Press. 198712 LI Z P. Int. J. Theor. Phys., 1993. 32: 20113 LI Z P. JIANG J H. Symmetries in Constrained Canonid Systems, Beijing, Science Press, 200214 LI Z P, GAO H X. Int. J. Theor. Phys., 1997, 36: 107115 LI Z P, Chinese Science Bulletin, 1999, 44: 20716 Deser S, Jackiw R, Templeton S. Ann. Phys., 1982, 140: 37217 Sundermeyer K. Lecture Notes in Physics. 169. Berlin. Springer-Verlag, 198218 Fossats A. Manavella E, Repetro C et a]. Int. J. Theor. Phys., 1995, 34: 1037; J. Math. Phys., 1996, 37: 8419 LI Z P, LONG Z W. J. Phys., 1999, A32: 6391
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LI Zi-Ping. Noether Identities at the Quantum Level[J]. Chinese Physics C, 2002, 26(3): 230-238.
LI Zi-Ping. Noether Identities at the Quantum Level[J]. Chinese Physics C, 2002, 26(3): 230-238. shu
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Received: 2001-05-18
Revised: 1900-01-01
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Noether Identities at the Quantum Level

    Corresponding author: LI Zi-Ping,
  • College of Applied Science, Beijing Polytechnic University, Beijing 100022, China

Abstract: Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived. For the gauge-invariant system, the quantal Noether identities in configuration space have been also deduced. It is pointed out that in certain cases the quantal Noether identities may be converted to quantal conservation laws of the system. This method for obtaining the quantal conservation laws is significantly different from the first Noether theorem at the quantum level. The application to non-Abelian CS theories is studied, the quantal conserved BRS and PBRS charges are obtained, and these two conserved charges are totally different.

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