Bound-State Variational Wave Equation For Fermion Systems In QED

TL;DR

This paper develops a relativistic variational wave equation for fermion systems in QED, incorporating all orders of interactions and providing a rigorous foundation for calculating bound states and radiative corrections.

Contribution

It introduces a Hamiltonian variational method for QED that derives a relativistic two-fermion wave equation with an interaction kernel including all Feynman diagrams.

Findings

Derived a relativistic two-fermion wave equation from QED.

Calculated one-loop radiative corrections to binding energies.

Validated the approach in covariant Feynman gauge.

Abstract

We present a formulation of the Hamiltonian variational method for QED which enables the derivation of relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant M-matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying QFT for arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number $n$, and $l =J=0$. Our calculations are carried out in the explicitly covariant Feynman gauge.