Complementarity and phases in SU(3)

Abstract

Phase operators and phase states are introduced for irreducible representations of the Lie algebra su(3) using a polar decomposition of ladder operators. In contradistinction with su(2), it is found that the su(3) polar decomposition does not uniquely determine a Hermitian phase operator. We describe two possible ways of proceeding: one based in imposing SU(2) invariance and the other based on the idea of complementarity. The generalization of these results to SU(n) is sketched.

Published as part of a special issue on coherent states

References in corpus (4)

• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
• The Schwinger Representation of a Group: Concept and Applications
• Variations on a theme of Heisenberg, Pauli and Weyl