# A geometric structure underlying the interaction Hamiltonian of quantum electrodynamics

## TL;DR

This paper reveals a geometric framework underlying the interaction Hamiltonian in quantum electrodynamics, deriving key components from fundamental operators with simple geometric interpretations.

## Contribution

It introduces fundamental interaction operators and a superoperator to derive the interaction Hamiltonian's structure from geometric principles.

## Key findings

- Eight parts of the interaction Hamiltonian are derived from two fundamental operators.
- The fundamental operators map electron-positron pairs to photons and vice versa.
- A superoperator describes vacuum fluctuations within this geometric framework.

## Abstract

In this paper, a simple geometric structure is shown, which underlies the interaction Hamiltonian of quantum electrodynamics. Specifically, eight parts of the interaction Hamiltonian, corresponding to eight basic Feynman diagrams, are found derivable from two operators called fundamental interaction operators (FIOs), with the help of a superoperator that describes vacuum fluctuations. And, the two FIOs have the simple geometric meanings of mapping the state space of an electron-positron pair to that of a photon and the reverse.