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Complementarity and phases in SU(3)

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arxiv 1206.2507 v1 pith:7STB7XZ4 submitted 2012-06-12 math-ph math.MPquant-ph

Complementarity and phases in SU(3)

classification math-ph math.MPquant-ph
keywords phasecomplementaritydecompositionoperatorspolaralgebracontradistinctiondescribe
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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