Thermal boson expansions and dynamical symmetry

N.R. Walet, Abraham Klein

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In this paper we study collective excitations of many-particle systems at finite temperature. We use three distinct ensembles: a restricted canonical ensemble, the normal canonical ensemble and the grand canonical ensemble. We apply the method of thermo-field dynamics which replaces the computation of thermal averages by quantum mechanics in a doubled Hubert space. We show how the use of dynamical symmetries may simplify matters; this is illustrated for the Lipkin model. For each of the ensembles the thermal hamiltonian has dynamical symmetry SU(2) × SU(2). This symmetry is violated by the thermal vacuum, which does not lie within a single irrep of this dynamical symmetry group. We find that for the restricted canonical ensemble we can classify the thermal state by a single irrep of a larger group (SU(4)), of which SU(2) × SU(2) is a subgroup. In order to be able to discuss the collective excitations we construct a boson mapping for the generators of the algebra SU(4). This is used to evaluate the boson expansion of the thermal hamiltonian, including the thermal RPA, for both the normal and deformed phase. Since the hamiltonian has a more restricted symmetry than the irreps we find Goldstone modes corresponding to the extra symmetry and two bosons corresponding to the SU(2) × SU(2) dynamical symmetry. For the canonical ensemble we find that a classification according to SU(4) is also convenient, even though the thermal state has components in several irreps. In the case of the grand canonical ensemble we show that the relevant algebra is U(4), where the thermal vacuum is completely contained within one irrep of mixed type (particle-hole or covariant-contragradient). We also construct the boson mapping for this irrep and derive the thermal boson expansion.
Original languageEnglish
Pages (from-to)261-284
Number of pages24
JournalNuclear Physics, Section A
Issue number2
Publication statusPublished - Apr 1990


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