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Quantum Symmetry for a System with a Singular Lagrangian Containing Subsidiary Condition

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Abstract

The quantization for a system with a singular Lagrangian containing subsidiary constrained conditions in configuration space is studied. The system is called constrained singular system. In certain case, the constrained singular system can be brought into the theoretical framework of the constrained Hamilton system. A modified Dirac-Bergmann algorithm for the calculation of constraints in the system is deduced. The path integral quantization is formulated by using the Faddeev-Senjanovic scheme, and the classical/quantum Noether theorem in canonical formalism are also established for such a system. The application of the results to study the fractional spin in non-Abelian Chern-Simons theory is given. We make a precise investigation of the fractional spin for such a system at the quantal level. A simple example is presented to show that the connection between the symmetry and conservation law in classical theories in general is no longer preserved in quantum theories.

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Authors and Affiliations

  1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Y. Zhang & A. M. Du

  2. Department of Applied Physics, Beijing Polytechnic University, Beijing, China

    J. H. Jiang & Z. P. Li

  3. SIGMA Weather Group, State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, P.O. Box 8701, Beijing, 100190, China

    Y. Zhang & X. H. Zhao

Authors
  1. Y. Zhang
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  2. J. H. Jiang
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  3. Z. P. Li
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  4. A. M. Du
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  5. X. H. Zhao
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Correspondence to Y. Zhang.

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Zhang, Y., Jiang, J.H., Li, Z.P. et al. Quantum Symmetry for a System with a Singular Lagrangian Containing Subsidiary Condition. Int J Theor Phys 50, 3398–3414 (2011). https://doi.org/10.1007/s10773-011-0845-4

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  • DOI: https://doi.org/10.1007/s10773-011-0845-4

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