All Questions

I'm reading a bit about geometric quantization and, among the axioms of this construction, is one requiring that the operator $\hat f = -\textrm i \hbar \nabla _{X_f} + f$ associated to the classical ...

The questions Q1. What are simple ways to think mathematically about the physical meanings of the Planck constant? Q2. How does the Planck constant appear in mathematics of quantum mechanics? In ...

Let ($X,\omega$) be a symplectic manifold (phase space of some physical system). Consider the algebra $\mathcal{C}^{\infty}(X,\mathbb{R})$ of smooth functions on $X$ and $[\omega]\in \textrm{H}^{2}_{\...

I know that many symplectic geometers are interested in quantization as well. From what I understood, quantization isn't expected to be used as a tool to answer symplectic questions (as in ...

What could be a mathematical model of such physical wish? I'm looking for something sending a symplectic manifold $(M,\omega)$ to a Hilbert space $H_{M}$ with the following properties: 1- We should ...