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

We apply nonperturbative variational techniques to a relativistic scalar field theory in which heavy bosons (open-quote open-quote nucleons close-quote close-quote) 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 close-quote 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 Ansaetze 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. copyright 1996 The American Physical Society