Abstract
Based on the phase-space generating functionalof the Green function, the canonical Ward identities(CWI) under local, nonlocal, and global transformationsin phase space for a system with a regular and singular Lagrangian have been derived. Therelation of global canonical symmetries to conservationlaws at the quantum level is presented. The advantage ofthis formulation is that one does not need to carry out the integration over canonicalmomenta in a phase-space path (functional) integral asin the traditional treatment in configuration space. Ingeneral, the connection between global canonicalsymmetries and conservation laws in classical theories isno longer preserved in quantum theories. Applications ofour formulation to the non-Abelian Chern-Simons (CS)theory are given, and new forms for CS gauge-ghost field proper vertices and the quantal conservedangular momentum of this system are obtained; thisangular momentum differs from the classical one in thatone needs to take into account the contribution of angular momenta of ghost fields.
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REFERENCES
E. Noether, Nachr. Ges. Wiss. Gotingen Math. Phys. Kl. 1918, 235 (1918).
E. L. Hill, Rev. Mod. Phys. 23, 253 (1951).
H. Suura and B. L. Young, Phys. Rev. D 8, 4353 (1973).
T. Lhallabi, Int. J. Theor. Phys. 28, 875 (1989).
Z.-P. Li, Acta Phys. Sin. 41, 710 (1992).
Z.-P. Li, J. Phys. A: Math. Gen. 24, 4261 (1991).
Z.-P. Li, Phys. Rev. E 50, 876 (1994).
J. C. Ward, Phys. Rev. 77, 293 (1950).
Y. Takahashi, Nuovo Cimento 6, 371 (1957).
A. A. Slavnov, Theor. Math. Phys. 10, 99 (1972).
J. C. Taylor, Nucl. Phys. B 33, 436 (1971).
S. D. Joglekar, Phys. Rev. D 44, 3879 (1991).
G. S. Danilov, Phys. Lett. B 257, 285 (1991).
B. L. Young, Introduction to Quantum Field Theories (Science Press, Beijing, 1987).
T. D. Lee and C. N. Yang, Phys. Rev. 128, 885 (1962).
I. S. Gerstein, R. Jackiw, B. W. Lee, and S. Weinberg, Phys. Rev. D 3, 2486 (1971).
T. S. Du, H. C. Yin, and T. N. Ruan, Nucl. Phys. B 164, 103 (1980).
Z.-P. Li, Classical and Quantal Dynamics of Constrained System and Their Symmetry Properties, Beijing Polytechnic University, Beijing (1993).
M. M. Mizrahi, J. Math. Phys. 19, 298 (1978).
Z.-P. Li and C. Yang, J. Phys. A Math. Gen. 28, 5931 (1995).
Z.-P. Li, Europhys. Lett. 27, 563 (1994).
Y. P. Kuang and Y. P. Li, Phys. Energiae Fortis Phys. Nuclearis 4, 286 (1980).
E. S. Fradkin and M. Ya. Palchik, Phys. Lett. B 147, 86 (1984).
M. Ya. Palchik, Yad. Fiz. 42, 522 (1985).
Z.-P. Li, Sci. China A 36, 1212 (1993).
Z.-P. Li, Acta Phys. Sin. (Overseas Ed.) 3, 481 (1994).
Z.-P. Li, High Energy Phys. Nucl. Phys. 19, 157 (1994).
Z.-P. Li, Int. J. Theor. Phys. 26, 853 (1987).
P. A.M. Dirac, Lecture on Quantum Mechanics, Yeshiva University Press, New York (1964).
K. Sundermeyer, Lecture Notes in Physics, No. 169, Springer-Verlag, Berlin (1982).
D. M. Gitman and I. V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, Berlin (1990).
L. D. Faddeev, Theor. Math. Phys. 1, 1 (1970).
P. Senjanovic, Ann. Phys. (N.Y.) 100, 227 (1976).
W. Siegel, Phys. Lett. B 128, 397 (1983).
J. W. Van Holten, Phys. Lett B 200, 507 (1988).
Z.-P. Li, Int. J. Theor. Phys. 32, 201 (1993).
R. Banerjee, Phys. Rev. D 48, 2905 (1993); Nucl. Phys. B 419, 611 (1994).
J. K. Kim, W.-T. Kim, and H. Shin, J. Phys. A Math. Gen. 27, 6067 (1994).
A. Lerda, Anyons, Springer-Verlag, Berlin (1992).
A. Antillon, J. Escalona, G. Germat, et al., Phys. Lett. B 359, 327 (1995).
R. Banerjee and B. Chakraborty, Ann. Phys. (N.Y.) 247, 188 (1996).
A. Foussats, E. Manavella, C. Repetto, et al., Int. J. Theor. Phys. 34, 1037 (1995).
S. Deser, R. Jackiw, and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982).
Z. S. Man, Y. X. Chen, and K. Li, Commun Theor. Phys. 24, 491 (1995).
Z. P. Li, Int. J. Theor. Phys. 34, 523 (1995).
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Li, ZP., Jun, B. Canonical Symmetries in the Functional Formalism. International Journal of Theoretical Physics 38, 1677–1695 (1999). https://doi.org/10.1023/A:1026659014663
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DOI: https://doi.org/10.1023/A:1026659014663