标题： 非交换物理在李代数、Z_2^n格子和克利福德代数上 显示英文标题

标题： Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras

摘要： 我们调查坐标为李代数包络代数的非对易时空。 我们还解释如何对通过Moyal乘积类型的cocycle扭曲从对易时空得到的非对易空间进行微分几何，例如非对易环面， $\theta$-空间和 Clifford 代数。 后者是对有限格点$(\Z_2)^n$的非对易变形，我们计算它们的非对易 de Rham 上同调和麦克斯韦方程组解的模空间。 我们在路径积分方法中精确地对$\Z_2\times\Z_2$上的非对易 U(1)-Yang-Mills 理论进行量子化。 显示英文摘要

摘要： We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type cocycle twist, such as the noncommutative torus, $\theta$-spaces and Clifford algebras. The latter are noncommutative deformations of the finite lattice $(\Z_2)^n$ and we compute their noncommutative de Rham cohomology and moduli of solutions of Maxwell's equations. We exactly quantize noncommutative U(1)-Yang-Mills theory on $\Z_2\times\Z_2$ in a path integral approach.