Geometry of quantum mechanics

Quantum mechanics is formulated on the true space of physical states—the projective Hilbert space. It is found that the postulates of quantum mechanics assume an intrinsically geometric form. In particular, observables are represented by real‐valued functions, the Lie bracket on the space of observables is given by a Poisson structure, and the Schrödinger evolution is equivalent to the flow along a Hamiltonian vector field.