Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics

Ennio Gozzi

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arXiv · q-alg/9702032

Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics

Ennio Gozzi

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Abstract

In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bundle to phase-space. In this space we introduce an extended Poisson brackets structure which allows us to re-do all the usual Cartan calculus on symplectic manifolds via these brackets. We also briefly sketch how the Schouten-Nijenhuis, the Frölicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.

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Ennio Gozzi. 1997-02-26. Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics. https://arxiv.org/abs/q-alg/9702032

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