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arXiv · 0904.4291

The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds

Sooran Kang
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Abstract

In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that give rise to critical points of the Yang-Mills functional. Moreover, we show that this set of solutions can be described as a set of solutions to Laplace's equation on quantum Heisenberg manifolds.

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Sooran Kang. 2009-04-28. The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds. https://arxiv.org/abs/0904.4291

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