Hamiltonian anomalies of bound states in QED

TL;DR

This paper presents a Hamiltonian approach to bound states in QED, revealing anomaly-like contributions in processes such as parapositronium creation, using nonlocal representations and Dirac's quantization method.

Contribution

It introduces a systematic Hamiltonian framework for QED bound states employing nonlocal irreducible representations and demonstrates its application to specific processes like parapositronium creation.

Findings

Identification of anomaly-type contributions in parapositronium creation

Application of nonlocal representations to bound state quantization

Calculation of triangle diagram in QED bound states

Abstract

The Bound State in QED is described in systematic way by means of nonlocal irreducible representations of the nonhomogeneous Poincare group and Dirac's method of quantization. As an example of application of this method we calculate triangle diagram $Para-Positronium \to \gamma\gamma$. We show that the Hamiltonian approach to Bound State in QED leads to anomaly-type contribution to creation of pair of parapositronium by two photon.