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We apply nonperturbative variational techniques to a relativistic scalarfield theory in which heavy bosons (``nucleons'') interact with light scalarmesons via a Yukawa coupling. Integrating out the meson field and neglectingthe nucleon vacuum polarization one obtains an effective action in terms of theheavy particle coordinates which is nonlocal in the proper time. As inFeynman's polaron approach we approximate this action by a retarded quadraticaction whose parameters are to be determined variationally on the pole of thetwo-point function. Several ans\"atze for the retardation function are studiedand for the most general case we derive a system of coupled variationalequations. An approximate analytic solution displays the instability of thesystem for coupling constants beyond a critical value.Comment: 33 pages standard LaTeX, 3 uuencoded gzipped postscript figures  embedded with psfig.st

Polaron variational methods in the particle representation of field theory. I. General formalism