Shadow Hamiltonians, Poisson brackets, and gauge theories
Shadow Hamiltonians, Poisson brackets, and gauge theories
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影子哈密顿量、泊松括号和规范理论
DOI：
10.1103/physrevd.87.034511
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发表时间：
2012
影响因子：
5
通讯作者：
M. Clark
中科院分区：
文献类型：
--
作者：
A. D. Kennedy;P. Silva;M. Clark
数值格点规范理论计算产生规范场配置，包括动态费米子的影响，通常使用的算法，需要规范场的分子动力学演化使用辛积分。复杂的积分器是常用的，但很难优化，力梯度积分器显示出的承诺，特别是大晶格体积。我们解释说，辛积分导致非常有效的蒙特卡罗算法，因为他们正好保存一个影子哈密顿。阴影哈密顿量可以用泊松括号展开，并可用于优化积分器。我们展示了如何做到这一点可能是规范理论的扩展制定的哈密顿力学李群，包括泊松括号和阴影，并给出了一个通用的方法，实际计算的力量，力梯度，和泊松括号规范理论。
Numerical lattice gauge theory computations to generate gauge field configurations including the effects of dynamical fermions are usually carried out using algorithms that require the molecular dynamics evolution of gauge fields using symplectic integrators. Sophisticated integrators are commonly used but hard to optimize, and force-gradient integrators show promise especially for large lattice volumes. We explain that symplectic integrators lead to very efficient Monte Carlo algorithms because they exactly conserve a shadow Hamiltonian. The shadow Hamiltonian may be expanded in terms of Poisson brackets and can be used to optimize the integrators. We show how this may be done for gauge theories by extending the formulation of Hamiltonian mechanics on Lie groups to include Poisson brackets and shadows and by giving a general method for the practical computation of forces, force gradients, and Poisson brackets for gauge theories.