Cartan Calculus via Pauli Matrices

Details Cartan Calculus via Pauli Matrices Cartan Calculus via Pauli Matrices

2002-08-30

arxiv.org/abs/quant-ph/0208190v1

Int.J.Mod.Phys. A18 (2003) 5231-5260

Physics

Quantum Physics

30+1 pages, 1 figure

Scientific paper

10.1142/S0217751X03015982

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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