In this talk, we discuss the mean field quantum fluctuation dynamics for a system of infinitely many fermions with delta pair interactions in the vicinity of an equilibrium solution (the Fermi sea) at zero temperature in two and three dimensions. Our work extends some recent important results of M. Lewin and J. Sabin, who address the corresponding problem for more regular pair interactions. This is a joint work with Thomas Chen and Natasa Pavlovic at University of Texas at Austin.