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We discuss equivalent representations of the collective/bosonic Hamiltonianin the form of Taylor expansion over collective coordinate and momentum.Different expansions are equivalent if they are related by a transformation ofcollective variables. The independent parameters in the collective Hamiltonianare identified, which are much less in number than it appears. In this sense,the microscopic generalized density matrix method fixes the collectiveHamiltonian completely, which seems to solve the old problem of microscopiccalculation of the collective Hamiltonian.

Equivalent Representations of Collective Hamiltonian and Implication on Generalized Density Matrix Method