Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian

  • Based on the phase-space generating functional of a system with a singular Lagrangion,the Ward identities under global transformation in phase are deduced.The quantum conservation laws under the global symmetry transiormation are also derived which is in general different from classical Hoether's ones.The preliminary application of our formulation to the Yang-Mills theory the Ward-Takahashi identity and BRS conserved quantity for BRS transformation are presented.Applying to non-Abelian-Chern-Simons theory the quantum conserved angular momentum (QCAM) are obtained.The QCAM differs form classical one because the former needs to take into account the distribution of angular momentum of ghost innon-Abelian-Chern-Simons theory.
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  • [1] 李子平, 经典和量子约束系统及其对称性质, 北京工业大学出版社, 北京, 1993年.[2] L. D. Faddeev, Theor. Math. Phys., 1(1970)1.[3] P. Senjanovic, Ann. Phys., (NY), 100 (1976)227.[4] D. M. Gitman, I. V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, Berlin, 1991.[5] M. Henneaux, Phys. Reports, 126(1985) 1.[6] M. Hemeaux, C. Teilboim, Quantization of Gauge System, Princeton University Press, 1992.[7] H. Suura, B. L. Young, Phys. Rev., D8 (1973) 875.[8] B. L. Young, Introduction to Quantum Field Theories, Science Press, Beijing, 1987.[9] M. M. Mizrahi, J. Math. Phys., 19 (19781298.[10] T-I. Nishikawa, Phys. Lett., B309 (19931351.[11] 李子平, 高能物理与核物理, 18(1994)697.[12] Ziping Li, Int. J. Theor. Phys., 34 (1995)523.[13] W. Siegel, Phys. Lett., B128( 1983)397.[14] 李子平, 物理学报, 41 (1992)710.[15] K. Sundermeyer, Constrained Dynamics, Lecture Notes in Physics, 169, Springer-Verlag, Berlin, 1982.[16] A. Foussats. E. Manavella, C. Repetto et al., Int. J. Theor. Phys., 34(1995)1037.[17] R. Banerjee, Phys. Rev, D48 (1993) 2905; Nucl. Phys., B419(1994)611.[18] J. K. Kim, W-T. Kim, H. Shin , J. Phys., A: Math. Gen., 27(1994)6067.[19] A. Lerda, Anyons, Springer-Verlag, Berlin, 1992.
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Li Ziping. Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian[J]. Chinese Physics C, 1997, 21(1): 34-43.
Li Ziping. Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian[J]. Chinese Physics C, 1997, 21(1): 34-43. shu
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Received: 1900-01-01
Revised: 1900-01-01
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Global Symmetry in Phase-Space Path Integral for a System With a Singular Lagrangian

    Corresponding author: Li Ziping,
  • Department of Applied Physics,Beijing Polytechnic University,Beijing 100022

Abstract: Based on the phase-space generating functional of a system with a singular Lagrangion,the Ward identities under global transformation in phase are deduced.The quantum conservation laws under the global symmetry transiormation are also derived which is in general different from classical Hoether's ones.The preliminary application of our formulation to the Yang-Mills theory the Ward-Takahashi identity and BRS conserved quantity for BRS transformation are presented.Applying to non-Abelian-Chern-Simons theory the quantum conserved angular momentum (QCAM) are obtained.The QCAM differs form classical one because the former needs to take into account the distribution of angular momentum of ghost innon-Abelian-Chern-Simons theory.

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