Probing the mathematical nature of the photon field

TL;DR

This paper investigates the mathematical structure of the photon field in quantum electrodynamics, proposing that its degrees-of-freedom are linked to fermion states and confirming this by calculating the fine-structure constant.

Contribution

It introduces a novel assumption that the photon field's degrees-of-freedom are derived from fermion state space, and verifies this through numerical reproduction of the fine-structure constant.

Findings

Reproduces the numerical value of the fine-structure constant

Supports the idea that photon degrees-of-freedom are tied to fermion states

Provides a new perspective on the mathematical content of QED interaction terms

Abstract

The mathematical content of the interaction term of quantum electrodynamics is examined under the following assumption: It is presumed that the apparent degrees-of-freedom of the photon field reflect the kinematical degrees-of-freedom of the two-particle state space of massive fermions, rather than independent degrees-of-freedom of the photon field. This assumption is verified by reproducing the numerical value of the fine-structure constant.