论文标题
量子测量流和曲率
Quantum geodesic flows and curvature
论文作者
论文摘要
我们研究了在弯曲的量子riemannian几何形状上使用近期公式在双模块连接和完全正面图的曲子上流动的大地测量流。我们通过非交通矢量字段的规范$*$操作来完成这种形式主义。我们在经典的歧管上展示了Ricci张量如何在我们的方法中自然出现，这是在对流衍生物中的术语中，地球速度场差异的对流衍生物，并使用它来提出类似的对象。示例包括2 x 2矩阵，模糊球和$ q $ -sphere的代数上的量子测量流。
We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical $*$ operation on noncommutative vector fields. We show on a classical manifold how the Ricci tensor arises naturally in our approach as a term in the convective derivative of the divergence of the geodesic velocity field, and use this to propose a similar object in the noncommutative case. Examples include quantum geodesic flows on the algebra of 2 x 2 matrices, fuzzy spheres and the $q$-sphere.
