论文标题
沿轨道的狄拉克运算符的变形以及非紧密的哈密顿圆环歧管的量化
Deformation of Dirac operators along orbits and quantization of non-compact Hamiltonian torus manifolds
论文作者
论文摘要
我们给出了沿着可能非压缩歧管的组动作轨道的轨道轨道的变形的表述，以获取代表索引的模棱两可的索引和k个学周期。我们将此框架应用于非紧凑型汉密尔顿圆环歧管，以从索引理论的角度定义几何量化。我们提供两个申请。第一个是[q，r] = 0类型定理的证明，可以将其视为Abelian案例的Vergne猜想的证明。另一个是在非紧凑型环境中用于复曲面的Danilov型公式，这表明该几何量化与极化的选择无关。证据基于将索引定位到晶格点。
We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact Hamiltonian torus manifolds to define geometric quantization from the view point of index theory. We give two applications. The first one is a proof of a [Q,R]=0 type theorem, which can be regarded as a proof of the Vergne conjecture for Abelian case. The other is a Danilov-type formula for toric case in the non-compact setting, which shows that this geometric quantization is independent of the choice of polarization. The proofs are based on the localization of index to lattice points.
