Mathematical Sciences: Geometric Yang-Mills Theory

点击翻译按钮获取中文摘要

The principal investigator will continue his study of the geometry of the Yang-Mills moduli space. This will include an analysis of the semiclassical measure on moduli space with fermions added, and Donaldson invariants in terms of differential forms. He will also investigate a general approach to establishing the existence of non-minimal Yang-Mills fields on 4- manifolds with symmetry. In the early 1980s S.K.Donaldson showed the intimate connection between solutions of the Yang-Mills equations and differentiable structures on four-dimensional space. This discovery meant that two four-dimensional space-times could be topologically the same (have the same shape) but be differentiably distinct. No experiments have been devised to discover which of these differentiable structures describes our space-time. The principal investigator will continue his analysis of the ramifications of Donaldson's discoveries.