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arXiv math-ph/9810015math-phmath.MP
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非对易几何中Chern-Simons action的规范不变性

Gauge invariance of the Chern-Simons action in noncommutative geometry

T. Krajewski

备注：
Latex, 14 pages, To appear in the Proceeeding of the ISI GUCCIA workshop "Quantum groups, noncommutative geometry and fundamental physical interactions", D. Kastler and M. Rosso editors
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摘要：

与经典情形完全类似，我们在非对易几何中定义了Chern-Simons作用泛函，并研究了它在规范变换下的性质。通常，后者与规范变换群的连通性有关。我们建立了这个结果，利用循环上同调和K-理论之间的耦合，并证明，使用指数定理，这种耦合的情况下，非交换环面量子化。

英文摘要：

In complete analogy with the classical case, we define the Chern-Simons action functional in noncommutative geometry and study its properties under gauge transformations. As usual, the latter are related to the connectedness of the group of gauge transformations. We establish this result by making use of the coupling between cyclic cohomology and K-theory and prove, using an index theorem, that this coupling is quantized in the case of the noncommutative torus.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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