Cartan Calculus via Pauli Matrices
arXiv:quant-ph/0208190 · doi:10.1142/S0217751X03015982
Abstract
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.
30+1 pages, 1 figure