Quantum effective actions from nonperturbative worldline dynamics

We demonstrate the feasibility of a nonperturbative analysis of quantum fieldtheory in the worldline formalism with the help of an efficient numericalalgorithm. In particular, we compute the effective action for asuper-renormalizable field theory with cubic scalar interaction in fourdimensions in quenched approximation (small-$N_f$ expansion) to all orders inthe coupling. We observe that nonperturbative effects exert a strong influenceon the infrared behavior, rendering the massless limit well defined in contrastto the perturbative expectation. Our numerical method is based on a direct useof probability distributions for worldline ensembles, preserves all Euclideanspacetime symmetries, and thus represents a new nonperturbative tool for aninvestigation of continuum quantum field theory.Comment: 33 pages, 10 figure