Propagator from nonperturbative worldline dynamics

Abstract

We use the worldline representation for correlation functions together with numerical path integral methods to extract nonperturbative information about the propagator to all orders in the coupling in the quenched limit (small-N f expansion). Specifically, we consider a simple two-scalar field theory with cubic interaction (S 2 QED) in four dimensions as a toy model for QED-like theories. Using a worldline regularization technique, we are able to analyze the divergence structure of all-order diagrams and to perform the renormalization of the model nonperturbatively. Our method gives us access to a wide range of couplings and coordinate distances. We compute the pole mass of the S 2 QED electron and observe sizable nonperturbative effects in the strong-coupling regime arising from the full photon dressing. We also find indications for the existence of a critical coupling where the photon dressing compensates the bare mass such that the electron mass vanishes. The short distance behavior remains unaffected by the photon dressing in accordance with the power-counting structure of the model.

Non-perturbative Quantum Propagators in Bounded Spaces

“…This information can be useful for analytic and numerical estimations of the kernel for systems whose path integral cannot be computed in close form, since it can indicate which trajectories, or regions of space, will be dominant in its determination. In fact the hit function was already sampled in works based on worldline numerics [4] and the extension considered here could shed new light on the undersampling problem encountered in [35][36][37]. Looking further ahead, the methods we describe here are well-adapted to the problem of estimating the Casimir energy for arbitrary surface geometries, even for partially conducting plates.…”

A Monte Carlo approach to the worldline formalism in curved space

“…now known as Worldline Monte Carlo (WLMC) and have been used for several application in QFT, such as the Casimir effect [26], Schwinger pair production in inhomogeneous fields [27], quantum effective actions [28], strongly-coupled, large-N fermion models [29], and the nonperturbative propagator of scalar, QED-like, theories [30]. In these works, all the proposed algorithms are based on a Monte Carlo sampling which models the free Brownian motion.…”

The Generalised LKF Transformations for Arbitrary $N$-point Fermion Correlators

“…By now it is recognised that the worldline formalism has several advantages over standard methods, including representations of amplitudes where virtual momenta have already been integrated over that combine multiple Feynman diagrams related by permutation of external legs [31,69,[71][72][73] and are gauge invariant even at the level of the integrand [65,68]. Initial work using worldline techniques was largely focussed on loop amplitudes and although there are a few preliminary representations of propagators and tree-level processes using worldline techniques [71,[74][75][76][77][78][79], it is only recently that a complete description of the scalar [60,61,[80][81][82][83][84], spinor [85][86][87][88] and quark [89,90] propagators that are needed to study the LKF transformations has been achieved that retains the familiar benefits of the first quantised approach (see also [91]).…”