Matrix Theory from Schild Action

Starting from the Schild action for membrane, we present an alternative formulation of Matrix Theory. First of all, we construct the Schild action for general bosonic p-brane which is classically equivalent to the Nambu-Goto action for p-brane. Next, based on the constraint obtained from the variational equation for the auxiliary field in the case of $p = 2$ (membrane), we construct a new matrix model which is closely related to the matrix model of M-theory as developed by Banks, Fischler, Shenker and Susskind (BFSS). Our present formulation is a natural extension of the construction of type IIB matrix model by Yoneya to the case of M-theory.