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

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

2003-10-29

arxiv.org/abs/math-ph/0310065v2

Physics

Mathematical Physics

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

Scientific paper

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 ${\cal R} = {\mathbb C}P^n$. The connection between the two is discussed.

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