Riemannian structure on manifolds of quantum states

摘要: A metric tensor is defined from the underlying Hilbert space structure for any submanifold of quantum states. The case where manifold generated by action a Lie group on fixed state vector (generalized coherent states hereafter noted G.C.S.M.) studied in details; geometrical properties some wellknown G.C.S.M. are reviewed and an explicit expression scalar Riemannian curvature given general case. physical meaning such structures (which have been recently introduced to describe collective manifolds nuclear physics) discussed. It shown examples that distance between nearby related fluctuations; particular harmonic oscillator condition zero appears be identical non dispersion wave packets.