Coherent loop states and angular momentum

TL;DR

This paper explores Bohr-Sommerfeld states within SU(2) representations, linking classical and quantum angular momentum, and derives asymptotic formulas for inner products and Wigner matrix elements.

Contribution

It provides a rigorous analysis of coherent loop states in SU(2), connecting classical and quantum angular momentum, and proves key asymptotic formulas in this context.

Findings

Recovered the standard angular momentum basis from coherent loop states

Proved the asymptotics of inner products of coherent loop states

Derived the asymptotics of Wigner matrix elements using geometric formulas

Abstract

We study Bohr-Sommerfeld states in the context of the irreducible representations of SU(2). These states offer a precise bridge between the classical and quantum descriptions of angular momentum. We show that they recover the usual basis of angular momentum eigenstates used in physics, and give a self-contained proof in this setting of the formula of Bothwick, Paul and Uribe for the asymptotics of the inner product of arbitrary coherent loop states. As an application, we use these states to derive Littlejohn and Yu's geometric formula for the asymptotics of the Wigner matrix elements.