  Monte Carlo techniques with importance sampling have been extensively applied
to lattice gauge theory in the Lagrangian formulation. Unfortunately, it is
extremely difficult to compute the excited states using the conventional Monte
Carlo algorithm. Our recently developed approach: the Monte Carlo Hamiltonian
method, has been designed to overcome the difficulties of the conventional
approach. In this paper, we extend the method to many body systems and quantum
field theory. The Klein-Gordon field theory is used as a testing ground.
