Classical and quantum mechanics via supermetrics in time

Details Classical and quantum mechanics via supermetrics in time Classical and quantum mechanics via supermetrics in time

2009-10-09

arxiv.org/abs/0910.1812v1

Found.Phys.40:795-806,2010

Physics

Quantum Physics

To appear in the proceedings of the conference held in Trieste in October 2008 with title: "Theoretical and Experimental aspec

Scientific paper

10.1007/s10701-009-9355-0

Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechanics. 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 metric in this supermanifold and show that a particular choice of the supermetric reproduces the CPI while a different one gives the QPI.

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