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

TL;DR

This paper explores different equivalent forms of the collective Hamiltonian using Taylor expansions and shows how the generalized density matrix method can uniquely determine it, addressing a longstanding problem in microscopic calculations.

Contribution

It demonstrates the equivalence of various collective Hamiltonian representations and shows how the generalized density matrix method can fully determine the Hamiltonian.

Findings

Different expansions are equivalent if related by a transformation of variables.

The number of independent parameters in the Hamiltonian is smaller than previously thought.

The generalized density matrix method can fix the Hamiltonian completely.

Abstract

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