The tunneling of a particle between two states, as influenced by coupl
ing the particle to an external field, is investigated. A spin-boson H
amiltonian is used to describe the tunnel system and its interaction w
ith a medium and is augmented by a term coupling the dipole moment of
the particle to the external held. A projection operator method is int
roduced that provides equations of motion for the particle's density m
atrix and permits discussion of external held effects on tunneling eve
n at very low temperatures. These equations of motion can exhibit solu
tions characterized by population relaxation with a rate constant that
is an average over the period of the external held. As an application
of this theory, the modification by an external field of the tunnelin
g rate of a defect in a metal, where the system-medium interaction is
characterized by an Ohmic spectrum, is evaluated. At sufficiently low
temperatures, for experimentally relevant parameter values, suitably c
hosen (constant and/or sinusoidal), external fields can greatly suppre
ss or enhance the tunneling rate relative to the field-independent val
ue.