Geometric Quantization (55 Years Later)

The standard textbook formalism of quantum mechanics is based on the global, flat structure of physical space (or space-time in its relativistic version). The theory of geometric quantization, which began with J. M. Souriau’s classic book, is the first attempt to free quantum physics from this global structure and formulate it in a more geometric, coordinate-independent way. The present article proposes a new formalism of geometric quantization, adapted to the analysis of problems that theoretical physicists encounter in their everyday work. The article attempts to check: “To what extent is quantum theory compatible with geometry?”.