  We apply nonperturbative variational techniques to a relativistic scalar
field theory in which heavy bosons (``nucleons'') interact with light scalar
mesons via a Yukawa coupling. Integrating out the meson field and neglecting
the nucleon vacuum polarization one obtains an effective action in terms of the
heavy particle coordinates which is nonlocal in the proper time. As in
Feynman's polaron approach we approximate this action by a retarded quadratic
action whose parameters are to be determined variationally on the pole of the
two-point function. Several ans\"atze for the retardation function are studied
and for the most general case we derive a system of coupled variational
equations. An approximate analytic solution displays the instability of the
system for coupling constants beyond a critical value.
