THE TRANSLATION-INVARIANCE AND THE VANISHING RENORMALIZATION COEFFICIENT IN AN INTERACTING LATTICE FERMION OR BOSON SYSTEM

Recently, by using the spin wave theory, some authors [14] calculated analytically the renormalization coefficient of a simplified strongly correlated lattice Fermion system and obtained a nonvanishing value in the thermodynamic limit. In this article, under the assumption of the translation invariance, we shall show that this coefficient is, in fa ct, zero for an interacting lattice Fermion system. Our result is cons istent with Anderson's proposition [13]. Finally, we discuss briefly o n the similar problem for an interacting lattice boson system.