Abstract
Field theories are widely used in areas including high energy, cosmology and condensed matter physics. These applications are growing ever more demanding. However, a gap exists between the standard perturbation theory methods (Feynman diagrams) and large scale “black box” Monte Carlo simulations. n-particle irreducible effective actions (nPIEA) are powerful non-perturbative tools which fill the gap by summing certain subsets of Feynman diagrams to infinite order. Unfortunately, many important properties of field theories depend on order-by-order cancellations (e.g. symmetries, gauge invariances, supersymmetries, unitarity, etc.) which are “brittle” under approximations of nPI effective actions. We have extended a method recently developed by Pilaftsis and Teresi[2] which is designed to restore all symmetries in the nPI formalism. Our extension sums more Feynman diagrams and enforces more of the symmetry, and suggests an extension to gauge theories.
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