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See detailOn the exact solutions of the Lipkin-Meshkov-Glick model
Debergh, N.; Stancu, Floarea ULg

in Journal of Physics : A Mathematical & General (2001), A34

We present the many-particle Hamiltonian model of Lipkin, Meshkov and Glick in the context of deformed polynomial algebras and show that its exact solutions can be easily and naturally obtained within ... [more ▼]

We present the many-particle Hamiltonian model of Lipkin, Meshkov and Glick in the context of deformed polynomial algebras and show that its exact solutions can be easily and naturally obtained within this formalism. The Hamiltonian matrix of each $j$ multiplet can be split into two submatrices associated to two distinct irreps of the deformed algebra. Their invariant subspaces correspond to even and odd numbers of particle-hole excitations. [less ▲]

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See detailOn Relativistic Scalar and Vector-Mesons with Harmonic Oscillator-Like Interactions
Debergh, N.; Ndimubandi, J.; Strivay, David ULg

in Zeitschrift Fur Physik C-Particles and Fields (1992), 56(3), 421-425

Relativistic descriptions for spin 0 and 1 particles of nonzero restmasses are known for a long time as the so-called Kemmer or Sakata-Taketani formulations. Through harmonic oscillatorlike interactions ... [more ▼]

Relativistic descriptions for spin 0 and 1 particles of nonzero restmasses are known for a long time as the so-called Kemmer or Sakata-Taketani formulations. Through harmonic oscillatorlike interactions, we study the nonrelativistic limit of the corresponding wave equations in connection with expected spin-orbit terms. Typical Foldy-Wouthuysen developments are included in these approaches with exact results up to required orders for interacting vector mesons only. [less ▲]

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