Introduction to Quantum Mechanics and the Quantum-Classical transition
Quantum Physics
2007-07-25 v1
Abstract
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the action of the unitary group on the Hilbert space allows to relate both approaches. We also study Weyl-Wigner approach to Quantum Mechanics and discuss the implications of bi-Hamiltonian structures at the quantum level.
Cite
@article{arxiv.0707.3539,
title = {Introduction to Quantum Mechanics and the Quantum-Classical transition},
author = {J. F. Carinena and J. Clemente-Gallardo and G. Marmo},
journal= {arXiv preprint arXiv:0707.3539},
year = {2007}
}
Comments
Survey paper based on the lectures delivered at the XV International Workshop on Geometry and Physics Puerto de la Cruz, Tenerife, Canary Islands, Spain September 11-16, 2006. To appear in Publ. de la RSME