Some Physical Appearances of Vector Coherent States and CS Related to Degenerate Hamiltonians

In the spirit of some earlier work on the constructionof vector coherent states over matrix domains, we compute heresuch states associated to some physical Hamiltonians. Inparticular, we construct vector coherent states of theGazeau-Klauder type. As a related problem, we also suggest a wayto handle degeneracies in the Hamiltonian for building coherentstates. Specific physical Hamiltonians studied include a singlephoton mode interacting with a pair of fermions, a Hamiltonianinvolving a single boson and a single fermion, a charged particlein a three dimensional harmonic force field and the case of atwo-dimensional electron placed in a constant magnetic field,orthogonal to the plane which contains the electron. In this lastexample, which is related to the fractional quantum Hall effect,an interesting modular structure emerges for two underlying vonNeumann algebras, related to opposite directions of the magneticfield. This leads to the existence of coherent states built out ofKMS states for the system.