✦ LIBER ✦

Connes’ spectral triple and U(1) gauge theory on finite sets

✍ Scribed by Liangzhong Hu; Adonai S. Sant’Anna

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 95 KB
Volume: 42
Category: Article
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(01)00093-6

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✦ Synopsis

We first apply Connes' noncommutative geometry to a finite point set. The explicit form of the action functional of U( 1) gauge field on this n-point set is obtained. We then construct the U(1) gauge theory on a disconnected manifold consisting of n copies of a given manifold. In this case, the explicit action functional of U(1) gauge field is also obtained.