  In the spirit of some earlier work on the construction of vector coherent
states over matrix domains, we compute here such states associated to some
physical Hamiltonians. In particular, we construct vector coherent states of
the Gazeau-Klauder type. As a related problem, we also suggest a way to handle
degeneracies in the Hamiltonian for building coherent states. Specific physical
Hamiltonians studied include a single photon mode interacting with a pair of
fermions, a Hamiltonian involving a single boson and a single fermion, a
charged particle in a three dimensional harmonic force field and the case of a
two-dimensional electron placed in a constant magnetic field, orthogonal to the
plane which contains the electron. In this last example, an interesting modular
structure emerges for two underlying von Neumann algebras, related to opposite
directions of the magnetic field. This leads to the existence of coherent
states built out of KMS states for the system.
