Lie Symmetry of Constrained Hamiltonian Systems and Its Application in Field Theory

ZHOU Jingrun; FU Jingli

doi:10.21656/1000-0887.390218

Volume 40 Issue 7

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ZHOU Jingrun, FU Jingli. Lie Symmetry of Constrained Hamiltonian Systems and Its Application in Field Theory[J]. Applied Mathematics and Mechanics, 2019, 40(7): 810-822. doi: 10.21656/1000-0887.390218

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Lie Symmetry of Constrained Hamiltonian Systems and Its Application in Field Theory

doi: 10.21656/1000-0887.390218

ZHOU Jingrun^1,2,
FU Jingli^1,2

¹Science Teaching and Research Section, Shaoxing Vocational and Technical College,Shaoxing, Zhejiang 312000, P.R.China;²Institute of Mathematical Physics, Zhejiang SciTech University,Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China(11272287;11872335;11472247)

Received Date: 2018-08-07
Rev Recd Date: 2018-09-07
Publish Date: 2019-07-01

Abstract

Abstract

The Lie symmetry method was studied for constrained Hamiltonian systems, and the conservation laws of the field theory systems were obtained. Firstly, the generalized canonical equations for constrained Hamiltonian systems were derived. Secondly, the determining equations and structural equations about the Lie symmetry of the constrained Hamiltonian systems were deduced. Thirdly, the Lie theorems and the conserved quantities for constrained Hamiltonian systems were given. Finally, the Lie symmetry for the system of the complex scalar field coupled to the Chern-Simons term was discussed. Two examples in the field theory illustrate the validity of this method.
- Lie symmetry,
- constrained Hamiltonian system,
- field theory,
- conserved quantity

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References(51)

References

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