A holomorphic representation approach to the regularization of model field theories in coupled cluster form

Jouko S. Arponen, Raymond F. Bishop

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    Abstract

    We explain in detail the so-called Bargmann or holomorphic representation, and apply it to the general class of single-mode bosonic field theories. Since these model field theories have no attribute of separability and are, in some sense, maximally nonlocal, they are an especially severe test of the capability of coupled cluster methods to parametrize them satisfactorily. They include the cases of anharmonic oscillators of order 2K (K=2, 3,...), for which ordinary perturbation theory is known to diverge, and we therefore make a special study of such systems. We demonstrate for the first time for any quantum-mechanical problem with infinite Hilbert space that both the normal and extended coupled cluster methods (NCCM and ECCM) have phase spaces which rigorously exist. We analyze completely the asymptotic properties of the complete sets of the NCCM and ECCM amplitudes, either of which fully characterizes the system. It is thereby shown how the holomorphic representation can be used to regularize completely all otherwise formally divergent series that appear. We demonstrate in detail how the entire NCCM and ECCM programmes can be carried through for these systems, including the diagonalization of the classically mapped Hamilitonians in the respective classical NCCM and ECCM phase spaces.
    Original languageEnglish
    Pages (from-to)289-305
    Number of pages17
    JournalTheoretica Chimica Acta
    Volume80
    DOIs
    Publication statusPublished - 1991

    Keywords

    • Anharmonic oscillators
    • Bargmann space
    • Coupled cluster theory
    • Extended coupled cluster method
    • Holomorphic representation
    • Model field theories
    • Normal coupled cluster method
    • Regularization

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