The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds |
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Authors: | Sooran Kang |
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Institution: | Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO 80309, United States |
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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 gives rise to critical points of the Yang-Mills functional. Moreover, we show that there is a relationship between this particular family of critical points of the Yang-Mills functional and Laplace's equation on multiplication-type, skew-symmetric elements of quantum Heisenberg manifolds; recall that Laplacian is the leading term for the coupled set of equations making up the Yang-Mills equation. |
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Keywords: | The Yang-Mills functional Quantum Heisenberg manifolds Laplace's equation |
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