  A Hamiltonian analysis of models given by a three-form field with a generic
potential coupled to general relativity in four dimensions is performed. This
kind of fields are naturally present in string theory and cosmological
scenarios. In particular, the action that will be considered has been
extensively used during the last years to propose inflationary and dark energy
models. Nevertheless, in order to keep the discussion as generic as possible,
neither symmetries nor a specific form of the potential for the three-form
field will be imposed. Interesting and relevant results about the number of
dynamical degrees of freedom of these models are obtained. In addition, the
analogy with a weakly-coupled scalar field is discussed. Finally, as a
particular example of this generic framework, the homogeneous and isotropic
cosmological case will be presented.
