Hamiltonian formulation of generalized quantum dynamics |
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Authors: | Ning Wu Tunan Ruan |
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Institution: | (1) CCAST (World Lab), 100080 Beijing, China;(2) Department of Physics, University of Science and Technology of China, 230026 Hefei, China |
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Abstract: | The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed.
After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations
of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion
of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations
of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total
trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding
Heisenberg equations.
Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph.
D. Directing Programme of Chinese University, and the Chinese Academy of Sciences. |
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Keywords: | Poisson bracket total trace Hamiltonian equation of motion canonical quantization condition |
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