Singlet-Triplet Splitting of Positronium in Light-Front QED

TL;DR

This paper calculates the singlet-triplet ground state spin splitting in positronium using a light-front Hamiltonian approach, confirming its consistency with traditional methods at leading order in QED.

Contribution

It provides a simplified analytical method to compute positronium spin splitting in light-front QED, demonstrating equivalence with equal-time approaches at leading order.

Findings

Analytical derivation of positronium spin splitting in light-front QED

Confirmation of approach equivalence at leading order

Simplified calculation method presented

Abstract

We study the QED bound-state problem in a light-front hamiltonian approach. It is important to establish the equivalence (or not) of equal-time and light-front approaches in the well-understood arena of Quantum Electrodynamics. Along these lines, the singlet-triplet ground state spin splitting in positronium is calculated. The well-known result, $(7/6) \alpha^2 Ryd$, is obtained analytically, which establishes the equivalence between the equal-time and light-front approaches (at least to this order). The true equivalence of the two approaches can only be established after higher-order calculations. It was previously shown that this light-front result could be obtained analytically, but a simpler method is presented in this paper.