A new theoretical analysis of the conductivity tensor is developed by use o
f the composite operator method for the two-dimensional Hubbard model. With
the aid of the Ward-Takahashi identities which phrase the charge conservat
ion law, the calculation of the current-current propagator is reduced hiera
rchically to the current-charge and charge-charge ones. Besides, the fermio
nic character of the propagating charges is preserved because of a constrai
ning equation with the content of the Pauli principle which uniquely fixes
the single-particle dynamics. (C) 1999 Elsevier Science B.V. All rights res
erved.