N-quantum calculation of the hydrogen atom with one-photon exchange

TL;DR

This paper introduces the N-quantum approach (NQA) as a covariant, effective 3D method for calculating hydrogen atom energy levels and wave functions, providing a new alternative to traditional equations like Bethe-Salpeter.

Contribution

The paper demonstrates the application of NQA to the relativistic hydrogen atom, offering a systematic way to include corrections beyond Coulomb interaction in bound state calculations.

Findings

NQA yields normalizable bound state solutions.

Systematic corrections beyond Coulomb interaction are obtained.

Method is independent of Bethe-Salpeter equation.

Abstract

The N-quantum approach (NQA) to quantum field theory uses the complete and irreducible set of in or out fields, including in or out fields for bound states, as standard building blocks to construct solutions to quantum field theories. In particular, introducing in (or out) fields for the bound states allows a new way to calculate energy levels and wave functions for the bound states that is both covariant and effectively 3-dimensional. This method is independent of the Bethe-Salpeter equation. In contrast to the Bethe-Salpeter equation, all solutions of the NQA are normalizable and correspond to physical bound states. In this paper we use the NQA in one-loop approximation to calculate states of the relativistic hydrogen atom and analogous two-body systems to illustrate how our new method works. With additional terms in the in field expansion we find systematic corrections beyond the Coulomb interaction.