Complementarity and phases in SU(3)

Abstract

Phase operators and phase states are introduced for irreducible representations of the Lie algebra using a polar decomposition of ladder operators. In contradistinction with , it is found that the polar decomposition does not uniquely determine a Hermitian phase operator. We describe two possible ways of proceeding: one based on imposing SU(2) invariance and the other based on the idea of complementarity. The generalization of these results to SU(n) is sketched.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.