Spin Networks, Wilson Loops and 3nj Wigner Identities
Mathematical Physics
2021-11-30 v1 High Energy Physics - Lattice
High Energy Physics - Theory
math.MP
Abstract
We exploit the spin network properties of the magnetic eigenstates of SU(2) Hamiltonian lattice gauge theory and use the Wilson loop operators to obtain a wide class of new identities amongst 3nj Wigner coefficients. We also show that the topological ground states of the SU(2) toric code Hamiltonian lead to Wigner 3nj identities with non-trivial phases. The method is very general and involves only the eigenvalue equations of any gauge invariant operator and their solutions. Therefore, it can be extended to any higher dimensional spin networks as well as larger SU(N) groups.
Keywords
Cite
@article{arxiv.2111.14685,
title = {Spin Networks, Wilson Loops and 3nj Wigner Identities},
author = {Manu Mathur and Atul Rathor},
journal= {arXiv preprint arXiv:2111.14685},
year = {2021}
}
Comments
26 pages, 9 figures