We consider the dynamics of a charged particle in a space whose coordinates are $N\times N$ hermitian matrices. Putting things in the framework of D0-branes of String Theory, we mention that the transformations of the matrix coordinates induce non-Abelian transformations on the gauge potentials. The Lorentz equations of motion for matrix coordinates are derived, and it is observed that the field strengths also transform like their non-Abelian counterparts. The issue of the map between theory on matrix space and ordinary non-Abelian gauge theory is discussd. The phenomenological aspect of ``finite-N non-commutativity" for the bound states of D0-branes appears to be very attractive.
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机译：我们考虑一个带电粒子在其坐标为$ N \乘以N $厄米矩阵的空间中的动力学。将事物放在弦论的D0框架的框架中，我们提到矩阵坐标的变换在规范电势上引起了非阿贝尔变换。推导了矩阵坐标的洛伦兹运动方程，并且观察到场强也像非阿贝尔对应场一样发生变化。讨论了矩阵空间理论与普通非阿贝尔规范理论之间的映射问题。对于D0分子的束缚态，``有限N非交换性''的现象学方面似乎非常有吸引力。
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