  The tunneling Hamiltonian has proven to be a useful method in many body
physics to treat particle tunneling between different states represented as
wave functions. Here we present a generalization of the tunneling Hamiltonian
to quantum field theory, in which tunneling between states represented as wave
functionals of a scalar quantum field is considered. We examine quantum decay
of the false vacuum in the driven Sine-Gordon system, and show it is consistent
with the tunneling formalism derived here and matches up with the soliton -
anti soliton separation obtained from the Bogomil'nyi inequality. This
inequality permits construction of a gaussian wave functional representation of
soliton - anti soliton nucleated states and is consistent with respect to the
false vacuum hypothesis
