On the Leray-Maslov quantization of Lagrangian submanifolds (Q1317913)

The author defines a generalized Maslov index on the covering of order 4 of the Lagrangian Grassmannian \(\Lambda (n)\). This allows him to state Leray-Maslov's quantization rule independently of the choice of frame. In the particular case of the harmonic oscillator it yields to the energy levels predicted by quantum mechanics. In fact it has a great similarity with the classical Bohr-Sommerfeld quantization condition from old quantum mechanics.