On Nonperturbative Calculations in Quantum Electrodynamics

TL;DR

This paper introduces a new nonperturbative approach to quantum electrodynamics using an iterative scheme for Schwinger-Dyson equations, addressing gauge invariance, renormalization, and chiral symmetry breaking.

Contribution

It proposes a novel iterative method for nonperturbative QED calculations that incorporates gauge invariance and renormalization, and explores solutions related to chiral symmetry breaking.

Findings

The approach allows nonperturbative calculations despite the Landau pole.

Calculated terms for the vertex function expansion and anomalous magnetic moment.

Identified conditions for dynamical chiral symmetry breaking in different coupling regimes.

Abstract

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $\alpha$.