Properties of nuclear matter in cut-off field theory and renormalization group methods

The properties of nuclear matter are studied in the cut-off field theory. It is found that, under the Hartree approximation, the small cut-off makes the equations of state hard, especially at higher densities. The theory is modified in the framework of the renormalization group methods with arbitrary cut-off $\Lambda^\prime$. It is found that the expansion in terms of the $\sigma$ meson field is more favorable than the naive expansion of the inverse of $\Lambda^\prime$, when we do not use very large $\Lambda^\prime$.