Yang–Mills Theory over Compact Symplectic Manifolds

Author: Urakawa H.

Source: Annals of Global Analysis and Geometry, Volume 25, Number 4, June 2004 , pp. 365-402(38)

Publisher: Springer

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Abstract:

In this paper, Yang–Mills theory over a compact Kähler manifold is naturally extended to a compact symplectic manifold. The relation between the Yang–Mills equation and symplectic structure is explicitly clarified, and the moduli space of Yang–Mills connections over a compact symplectic manifold is constructed. Furthermore, the absolute minima of the Yang–Mills functional are characterized, and finite dimensionality of the moduli space of the minimizers of the Yang–Mills functional is shown.

Keywords: symplectic manifold; Yang–Mills connection; minimizer

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:AGAG.0000023246.97746.af

Affiliations: 1: Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Aoba 09, Sendai, 980-8579, Japan., Email: urakawa@math.is.tohoku.ac.jp

Publication date: 2004-06-01