Geometric phase and modulus relations for SU(n) matrix elements in the defining representation

Abstract

A set of relations between the modulus and phase is derived for amplitudes of the form $\mels{\hatu(x)}$ where $\hat{U}(x)\in SU(n)$ in the fundamental representation and $x$ denotes the coordinates on the group manifold. An illustration is given for the case $n=2$ as well as a brief discussion of phase singularities and superoscillatory phase behavior for such amplitudes. The present results complement results obtained previously \cite{PMrel1} for amplitudes valued on the ray space $\mathcal{R}=\mathbb{C}{P}^n$. The connection between the two is discussed.

9 Pages, RevTex 4, no figures. Corrected some typos and mistakes in equation referencing