On positronium states in ${\rm{QED_3}}$

TL;DR

This paper introduces a new method to analyze positronium states in QED3 using spectral representation and chain approximation, successfully calculating energy eigenvalues and electron mass consistent with existing results.

Contribution

It presents a novel approach combining spectral representation and chain approximation to determine positronium energy levels and electron mass in QED3.

Findings

Calculated energy eigenvalues of vector positronium states.

Determined electron physical mass at specific multi-valued function branches.

Results agree with previously known values.

Abstract

In this note, we present a new method to investigate the positronium states in ${\rm{QED_3}}$. According to the $\rm{K\ddot{a}ll\acute{e}n-Lehmann}$ spectral representation, the energy eigenvalues of bound states are poles of the correlation function. Using the chain approximation, we obtain the energy eigenvalues of the vector positronium states by taking into account the single-valued branches of multi-valued function. Using the same method, we also find the electron physical mass at some single-valued branch of multi-value function. Our results are agreement with the known ones.