Chern–Simons pre-quantizations over four-manifolds
Chern–Simons pre-quantizations over four-manifolds
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四流形上的 Chern-Simons 预量化
DOI：
10.1016/j.difgeo.2011.07.004
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发表时间：
2007
影响因子：
0.5
通讯作者：
Tosiaki Kori
中科院分区：
文献类型：
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作者：
Tosiaki Kori
我们赋予具有预辛结构的四流形上的SU(n)-主束上的连接空间，并定义了边界上平凡的规范变换组对其的哈密顿作用。然后我们考虑在四流形上n小于3的平凡SU(n)-主束这是一个零协同四流形的子流形，我们在平面连接的模空间上构建一个厄米特线束其曲率由前辛形式给出。这是模空间的chen - simons预量化。四流形边界上的规范变换群以一种无穷辛的方式作用于平面连接的模空间。当四流形是一个四维圆盘时，我们证明了这种作用通过它的李群扩展提升到预量化。后者的几何描述与四维Wess-Zumino-Witten模型有关。
We endow the space of connections on an SU(n)-principal bundle over a four-manifold with a pre-symplectic structure and define a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. Then we consider the trivial SU(n)-principal bundle for n⩾3 over the four-manifold that is a submanifold of a null-cobordant four-manifold, and we construct on the moduli space of flat connections a hermitian line bundle with connection whose curvature is given by the pre-symplectic form. This is the Chern–Simons pre-quantization of moduli spaces. The group of gauge transformations on the boundary of the four-manifold acts on the moduli space of flat connections by an infinitesimally symplectic way. When the four-manifold is a 4-dimensional disc we show that this action is lifted to the pre-quantization by its Lie group extension. The geometric description of the latter is related to the 4-dimensional Wess–Zumino–Witten model.