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

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

1997-02-26

arxiv.org/abs/q-alg/9702032v1

Rend.Sem.Mat.Univ.Politec.Torino 54 (1996) 269-277

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, amstex

Scientific paper

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 Fr\"olicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.

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