Boson, Symplectic and Other Replicas for Simple Hamiltonians

  • A. P. Zuker
  • M. Dufour
  • C. Pomar


We present a linearization method for some simple (naturally tridiagonal) Hamiltonians. For the ground states it is equivalent to the lowest approximation in the coupled cluster formalism and its extension to excited states is straightforward. Then we construct sets of equivalent Hamiltonians (boson or symplectic replicas) that produce the same secular problem. In general they are not manifestly Hermitian. We show how to deal with this problem and we extract mean fields that describe both the normal and symmetry breaking regimes and at the same time incorporate variationally terms usually thought of as correlations.


Difference Equation Linearization Method Commutation Rule Boson Operator Symplectic Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. CD87.
    M.C. Cambiaggio, J. Dukelsky, this volumeGoogle Scholar
  2. DPZ87.
    M. Dufour, C. Pomar and A.P. Zuker, CRN preprint available. To be submitted to Annals of Physics.Google Scholar
  3. KL81.
    A. Klein and C.T. Li, Phys. Rev. Lett. 46(1981) 895Google Scholar
  4. KLZ77.
    H. Kümmel, K.H. Lührmann and J.G.Zabolitzky, Phys. Rep. 36C(1978) 188Google Scholar
  5. LMG65.
    H.J. Lipkin, M. Meshkov and J.A. Glick, Nucl. Phys. 62 (1965) 188CrossRefGoogle Scholar
  6. LÜ77.
    K.H. Lührmann, Ann. of Phys. 103(1977) 253Google Scholar
  7. RS80.
    P. Ring, P. Shuck, The Nuclear Many Body Problem (Springer-Verlag) 1980)Google Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • A. P. Zuker
    • 1
  • M. Dufour
    • 1
  • C. Pomar
    • 2
  1. 1.Laboratoire de Physique Nucléare Théorique, C.R.N.Strasbourg CedexFrance
  2. 2.TANDAR, CNEABuenos AiresArgentina

Personalised recommendations