Variational Quantum Electrodynamics

TL;DR

This paper introduces a variational approach based on minimal variance for quantum electrodynamics, addressing renormalization and deriving finite integral equations for propagators, which can be solved iteratively.

Contribution

It develops a novel variational method suited for gauge fermions, providing a finite, iterative solution framework for QED propagators with exact UV divergence subtraction.

Findings

Renormalized propagators satisfy finite integral equations.

The method is proven viable with unique solutions.

Multi-dimensional equations are reduced to one-dimensional spectral equations.

Abstract

A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization is addressed, and the renormalized propagators are shown to be the solution of a set of finite integral equations. The method is proven to be viable and, by a spectral representation, the multi-dimensional integral equations are recast in one-dimensional equations for the spectral weights. The UV divergences are subtracted exactly, yielding a set of coupled Volterra integral equations that can be solved iteratively, and are known to have a unique solution.