Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechancs. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next we introduce a metrics in this supermanifold and show that a particular choice of the supermetrics reproduces the CPI while a different one gives the QPI.
Classical and Quantum Mechanics via Supermetric in Time
GOZZI, ENNIO
2009-01-01
Abstract
Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechancs. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for classical path-integral) to distinguish it from the quantum mechanical one, which we will indicate with QPI. In the CPI two Grassmannian partners of time make their natural appearance and in this manner time becomes something like a three dimensional supermanifold. Next we introduce a metrics in this supermanifold and show that a particular choice of the supermetrics reproduces the CPI while a different one gives the QPI.Pubblicazioni consigliate
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