Extending the Kostant–Souriau quantization map by “tautological-tuning” with symplectic and Riemannian structures

Though quantization is—from an ontological standpoint—a very strange operation, it seems unavoidable in the actual practice of physics. From a mathematical standpoint, canonical quantization was superseded decades ago by more elegant constructions, yet among practicing physicists it remains the de-facto champion among the many alternatives. Despite this fact, there is to this day no mathematically well-defined, coordinate independent construction that reproduces the results of canonical quantization for the most physically important phase space functions: position, momentum, angular momentum, and (quadratic) Hamiltonian functions. In this paper, I construct such a quantization map using standard structures from symplectic and Riemannian geometry in non-standard ways.