  An important quantity in quantum field theory is the vacuum-to-vacuum
transition amplitude in the presence of an external source. This quantity is
often designated by Z[J] and is the generator for the n-point Greens functions.
In textbooks Z[J] is often derived using a path integral formulation, however
it will be shown here that it is possible to derive Z[J] directly from the time
evolution operator without using the path integral formulation.
