2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/82653The 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 $Λ^\prime$. It is found that the expansion in terms of the $σ$ meson field is more favorable than the naive expansion of the inverse of $Λ^\prime$, when we do not use very large $Λ^\prime$.PACS numbers, 21.65.+fNuclear Theorytext