  The ground states of an abstract model in quantum field theory are
investigated. By means of the asymptotic field theory, we give a necessary and
sufficient condition for that the expectation value of the number operator of
ground states is finite, from which we obtain a wide-usable method to estimate
an upper bound of the multiplicity of ground states. Ground states of massless
GSB models and the Pauli-Fierz model with spin 1/2 are investigated as
examples.
