Coherent loop states and angular momentum

• URL: http://arxiv.org/abs/2306.17293v1
• Date: Thu, 29 Jun 2023 20:33:47 GMT
• Title: Coherent loop states and angular momentum
• Authors: Bruce Bartlett and Nzaganya Nzaganya
• Abstract summary: We study Bohr-Sommerfeld states in the context of the irreducible representations of SU(2). We show that they recover the usual basis of angular momentum eigenstates used in physics. As an application, we use these states to derive Littlejohn and Yu's geometric formula for thes of the Wigner matrix elements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

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