Worldline Monte Carlo with a fitted potential PDF gives an all-orders quenched propagator for S2QED, with a pole mass that drops toward zero near a critical coupling around 0.72.
Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism
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abstract
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.
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Propagator from Nonperturbative Worldline Dynamics
Worldline Monte Carlo with a fitted potential PDF gives an all-orders quenched propagator for S2QED, with a pole mass that drops toward zero near a critical coupling around 0.72.