Quantum Electrodynamics Mediated by a Photon with Generalized (Continuous) Spin

TL;DR

This paper develops a framework for calculating scattering amplitudes involving a photon with continuous spin, extending scalar QED to include non-zero spin Casimir, and analyzes their physical properties.

Contribution

It introduces rules for computing amplitudes with a continuous spin photon, generalizing scalar QED and exploring their unitarity and scaling behaviors.

Findings

Amplitudes reduce to scalar QED as $ ho o 0$

Computed pair annihilation and Compton scattering amplitudes with continuous spin photons

Analyzed unitarity and scaling properties at various $ ho$ values

Abstract

We present rules for computing scattering amplitudes of charged scalar matter and photons, where the photon has non-zero spin Casimir $\rho$, and is therefore a continuous spin particle (CSP). The amplitudes reduce to familiar scalar QED when $\rho\rightarrow 0$. As a concrete example, we compute the pair annihilation and Compton scattering amplitudes in this theory and comment on their physical properties, including unitarity and scaling behavior at small and large $\rho$.