Renormalized equations of motions for scalars and fermions in the 2PI formalism

TL;DR

This paper develops a renormalized on-shell scheme for the 2PI formalism applied to scalars and fermions, providing explicit formulas and efficient numerical methods for calculating two-point functions in various approximations.

Contribution

It introduces a renormalized on-shell scheme for the 2PI formalism, including explicit formulas and numerical schemes for scalars and fermions in different approximations.

Findings

Explicit counterterms for broken and unbroken phases.

Fast numerical convergence for two-point functions at large couplings.

Formulas for renormalized three- and four-point functions.

Abstract

We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phase. Moreover, we give explicit formulas for the renormalized three- and four-point functions in the broken phase. We then turn to the sunset approximation, with only scalars and then including fermions. We give explicit formulas for the wavefunction and mass counterterms. Moreover, we show that, in particular, the two-point functions can be obtained numerically in a fast converging scheme even for large couplings of order one.