论文标题
解决SU（3），SU（4）和SP（2）组的矩阵指数函数
Solving the matrix exponential function for the groups SU(3), SU(4) and Sp(2)
论文作者
论文摘要
$ su（2）$矩阵$ u = \ exp（i \ vecτ\！\ cdot \！\vecφ\，）= \ cos | \vecφ\，| + i \vecτ\！\ cdot \！ \hatφ\，\ sin | \vecφ\，| $ \\扩展到具有八个真实参数的$ su（3）$组。所得的分析公式涉及在立方方程的三个真实根上的总和，与所谓的不可减至的情况相对应，其中一个人必须采用角度的分解。当进入带有15个真实计划的特殊统一组$ su（4）$时，分析公式涉及四个四重程方程的四个真正根源的总和。具有三个正根的相关立方分解方程再次属于不可约的情况。此外，通过将相关条件强加于$ su（4）$矩阵，也可以使用十个真实参数来对待Symplectic Group $ sp（2）$。由于根部以两对相反的符号出现，因此这简化了$ sp（2）$矩阵的分析公式。还提供了$ SU（5）$，$ SU（6）$和$ sp（3）$的分析公式的前景。
The well known analytical formula for $SU(2)$ matrices $U = \exp(i \vec τ\!\cdot\! \vec φ\,) = \cos|\vec φ\,| + i\vec τ\!\cdot\! \hatφ\, \sin|\vec φ\,|$\\ is extended to the $SU(3)$ group with eight real parameters. The resulting analytical formula involves the sum over three real roots of a cubic equation, corresponding to the so-called irreducible case, where one has to employ the trisection of an angle. When going to the special unitary group $SU(4)$ with 15 real prameters, the analytical formula involves the sum over four real roots of a quartic equation. The associated cubic resolvent equation with three positive roots belongs again to the irreducible case. Furthermore, by imposing the pertinent condition on $SU(4)$ matrices one can also treat the symplectic group $Sp(2)$ with ten real parameters. Since there the roots occur as two pairs of opposite sign, this simplifies the analytical formula for $Sp(2)$ matrices considerably. An outlook to the situation with analytical formulas for $SU(5)$, $SU(6)$ and $Sp(3)$ is also given.
