The density manifold and configuration space quantization
The density manifold and configuration space quantization
The differential geometric structure of a Fréchet manifold of densities is developed, providing a geometrical framework for quantization related to Nelson's stochastic mechanics.The Riemannian and symplectic structures of the density manifold are studied, and the Schrödinger equation is derived from a variational principle.By a theorem of Moser, the density manifold …