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In the spirit of some earlier work on the construction of vector coherentstates over matrix domains, we compute here such states associated to somephysical Hamiltonians. In particular, we construct vector coherent states ofthe Gazeau-Klauder type. As a related problem, we also suggest a way to handledegeneracies in the Hamiltonian for building coherent states. Specific physicalHamiltonians studied include a single photon mode interacting with a pair offermions, a Hamiltonian involving a single boson and a single fermion, acharged particle in a three dimensional harmonic force field and the case of atwo-dimensional electron placed in a constant magnetic field, orthogonal to theplane which contains the electron. In this last example, an interesting modularstructure emerges for two underlying von Neumann algebras, related to oppositedirections of the magnetic field. This leads to the existence of coherentstates built out of KMS states for the system.Comment: 38 page

Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians