Quillen丛与Riemann曲面上非Abel涡旋的几何预量化
Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface
摘要：
本文给出了非交换涡旋的模空间。我们明确计算辛形式所产生的$L^2$度规，我们构建一个prequantum线丛的曲率是这个辛形式成正比。前量子线丛是具有修正的Quillen度量的Quillen行列式线丛。接下来，在交换涡的情况下，我们构造奎伦线丛的模空间的曲率形成一个家庭的辛形式参数化的$Ψ_0$，一个特定的丛的一部分。
英文摘要：
In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from the $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic form. The prequantum line bundle turns out to be Quillen's determinant line bundle with a modified Quillen metric. Next, as in the case of abelian vortices, we construct Quillen line bundles over the moduli space whose curvatures form a family of symplectic forms which are parametrised by $Ψ_0$, a section of a certain bundle.
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