nLab
quantization of the 2-sphere

Contents

Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Symplectic geometry

Contents

Idea

The 2-sphere with its standard volume form is canonically a Poisson manifold and in fact a symplectic manifold. As such it may be regarded as a simple example of a phase space of a mechanical system. The quantization of this system yields the corresponding quantum mechanical system. This turns out to be that of the degrees of freedom of a rotor or spinor in 3-dimensional Euclidean space (just the “internal” rotor/spin degrees of freedom, no translational motion).

Formalizations

Created on September 4, 2013 at 05:37:09. See the history of this page for a list of all contributions to it.