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

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

2009-04-28

arxiv.org/abs/0904.4291v1

Mathematics

Operator Algebras

19 pages

Scientific paper

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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