@article{Ashtekar1999GeometricalFO,
title={Geometrical Formulation of Quantum Mechanics},
author={A. Ashtekar and Troy A. Schilling},
journal={arXiv: General Relativity and Quantum Cosmology},
year={1999},
pages={23-65}
}

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a Uhler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics which, although equivalent to the standard algebraic formulation, has a very different appearance. In particular, states are now represented by points of a symplectic manifold (which happens to have in addition a compatible Riemannian metric), observables are… CONTINUE READING