dorsal/arxiv
View SchemaCartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics
| Authors | Ennio Gozzi |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9702032 |
| URL | https://arxiv.org/abs/q-alg/9702032 |
| Journal | Rend.Sem.Mat.Univ.Politec.Torino 54 (1996) 269-277 |
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 Fr\"olicher- Nijenhuis and the Nijenhuis-Richardson brackets look in our formalism.
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"abstract": "In this paper we review the recently proposed path-integral counterpart of\nthe Koopman-von Neumann operatorial approach to classical Hamiltonian\nmechanics. We identify in particular the geometrical variables entering this\nformulation and show that they are essentially a basis of the cotangent bundle\nto the tangent bundle to phase-space. In this space we introduce an extended\nPoisson brackets structure which allows us to re-do all the usual Cartan\ncalculus on symplectic manifolds via these brackets. We also briefly sketch how\nthe Schouten-Nijenhuis, the Fr\\\"olicher- Nijenhuis and the Nijenhuis-Richardson\nbrackets look in our formalism.",
"arxiv_id": "q-alg/9702032",
"authors": [
"Ennio Gozzi"
],
"categories": [
"q-alg",
"dg-ga",
"hep-th",
"math.DG",
"math.QA"
],
"journal_ref": "Rend.Sem.Mat.Univ.Politec.Torino 54 (1996) 269-277",
"title": "Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics",
"url": "https://arxiv.org/abs/q-alg/9702032"
},
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