论文标题
几何量化和量子力矩图上的Coadhexhexhine轨道和Kähler-Einstein歧管
Geometric quantization and quantum moment maps on coadjoint orbits and Kähler-Einstein manifolds
论文作者
论文摘要
Kähler歧管上的变形量化和几何量化给出了量子可观察到的代数和希尔伯特空间的数学描述，其中后来形成了通过Toeplitz Operators渐近地观察到的量子可观察到的表示。当Kähler歧管上有汉密尔顿$ g $ - $ g $ action时，量子代数和代表方面都存在相关的对称性。我们表明，在互惠轨道和Kähler-Einstein歧管的好情况下，这些对称性严格兼容（不仅渐近地）。
Deformation quantization and geometric quantization on Kähler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum observables asymptotically via Toeplitz operators. When there is a Hamiltonian $G$-action on a Kähler manifold, there are associated symmetries on both the quantum algebra and representation aspects. We show that in nice cases of coadjoint orbits and Kähler-Einstein manifolds, these symmetries are strictly compatible (not only asymptotically).
