标题： SU(3) 分子动力学模拟的修改后的凯莱变换 显示英文标题

标题： A modified Cayley transform for SU(3) molecular dynamics simulations

摘要： 我们提出对Cayley变换的一种修改，该变换为特殊酉群$\mathrm{SU}(3)$定义了合适的局部参数化。 新的映射用于构建相空间为$\mathrm{SU}(3)$的可分离哈密顿系统或更一般的$\mathrm{SU(3)}^N$、$N \in \mathbb{N}$的分裂方法。 特别关注在格点量子色动力学中规范场生成的混合蒙特卡洛算法。 我们证明，使用修改后的Cayley变换代替矩阵指数不会影响分裂方法的时间反演性和体积保持性。 此外，在纯规范场模拟中讨论并展示了基于Cayley的算法的优缺点。 显示英文摘要

摘要： We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose phase space is the cotangent bundle of $\mathrm{SU}(3)$ or, more general, $\mathrm{SU(3)}^N$, $N \in \mathbb{N}$. Special attention is given to the hybrid Monte Carlo algorithm for gauge field generation in lattice quantum chromodynamics. We show that the use of the modified Cayley transform instead of the matrix exponential neither affects the time-reversibility nor the volume-preservation of the splitting method. Furthermore, the advantages and disadvantages of the Cayley-based algorithms are discussed and illustrated in pure gauge field simulations.