基于泡利矩阵的Cartan演算
Cartan Calculus via Pauli Matrices
摘要：
本文将提供近年来发展起来的经典力学路径积分形式的一种新的可操作的对应形式。我们称之为新的，因为雅可比场和形式将通过有限维矩阵实现。作为一个副产品，我们将证明，所有的操作的Cartan演算，如外部的衍生物，内部压缩与向量场，李导数等，可以实现通过适当的张量积的泡利和单位矩阵。
英文摘要：
In this paper we will provide a new operatorial counterpart of the path-integral formalism of classical mechanics developed in recent years. We call it new because the Jacobi fields and forms will be realized via finite dimensional matrices. As a byproduct of this we will prove that all the operations of the Cartan calculus, such as the exterior derivative, the interior contraction with a vector field, the Lie derivative and so on, can be realized by means of suitable tensor products of Pauli and identity matrices.
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