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Quantum effective actions from nonperturbative worldline dynamics

H. Gies·J. Sánchez--Guillén·R. A. Vázquez
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Abstract

We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable field theory with cubic scalar interaction in four dimensions in quenched approximation (small-$N_f$ expansion) to all orders in the coupling. We observe that nonperturbative effects exert a strong influence on the infrared behavior, rendering the massless limit well defined in contrast to the perturbative expectation. Our numerical method is based on a direct use of probability distributions for worldline ensembles, preserves all Euclidean spacetime symmetries, and thus represents a new nonperturbative tool for an investigation of continuum quantum field theory.

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H. Gies, J. Sánchez--Guillén, R. A. Vázquez. 2005-05-31. Quantum effective actions from nonperturbative worldline dynamics. https://doi.org/10.1088/1126-6708%2F2005%2F08%2F067

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