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Cartan Calculus via Pauli Matrices

D. Mauro
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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.

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D. Mauro. 2002-08-30. Cartan Calculus via Pauli Matrices. https://doi.org/10.1142/s0217751x03015982

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