ABSTRACT
This chapter extrapolates the results of the subtraction of an external source term (or driving force) from the Hamiltonian to the case of a relativistic field theory, where there is a continuum of degrees of freedom at any given time. It assumes that in making the transition from classical field theory to quantum field theory, the classical field is replaced by an operator field in the Heisenberg picture, just as the transition from classical mechanics to non-relativistic quantum mechanics was made by replacing the classical variable. In the case of the free-field theory of a scalar field it is possible to evaluate the generating functional exactly. The chapter evaluates the generating functional approximately by expanding in powers of the coupling constant, starting from the exact result for the free-field theory.
