Reverse Engineering Approach to Quantum Electrodynamics

TL;DR

This paper proposes a novel approach to quantum electrodynamics by linking the empirical fine-structure constant to the structure of two-electron state space, suggesting it belongs to an irreducible Poincare group representation.

Contribution

It introduces a reverse engineering method that connects the empirical value of alpha to the theoretical structure of two-electron states in QED.

Findings

Calculated normalization factor matches Wyler's formula for alpha

Empirical alpha supports the irreducible two-particle Poincare representation

Provides a new perspective on the structure of two-electron states in QED

Abstract

The S matrix of e--e scattering has the structure of a projection operator that projects incoming separable product states onto entangled two-electron states. In this projection operator the empirical value of the fine-structure constant alpha acts as a normalization factor. When the structure of the two-particle state space is known, a theoretical value of the normalization factor can be calculated. For an irreducible two-particle representation of the Poincare group, the calculated normalization factor matches Wyler's semi-empirical formula for the fine-structure constant alpha. The empirical value of alpha, therefore, provides experimental evidence that the state space of two interacting electrons belongs to an irreducible two-particle representation of the Poincare group.