Calculation of the expectation values of the spin and the magnetic moment of the gamma photons created as a result of the electron-positron annihilation

TL;DR

This paper calculates the expectation values of spin and magnetic moment of gamma photons from electron-positron annihilation, revealing magnetic moment properties that could influence Stern-Gerlach experiments and understanding of polaritons.

Contribution

It introduces a novel calculation of gamma photon magnetic moments based on helicity, challenging the traditional view that spin is the key property in Stern-Gerlach experiments.

Findings

Gamma photons have magnetic moments aligned with their propagation direction.

The magnetic moments depend on the photon helicity (+ or -).

Predicted beam splitting in Stern-Gerlach experiments due to magnetic moments.

Abstract

We have calculated the expectation values of the spin and the intrinsic magnetic moment of the gamma photons created as a result of the electron-positron annihilation. We show that, depending on its helicity a gamma photon propagating in z direction with an angular frequency carries a magnetic moment of along the propagation direction. Here the (+) and (-) signs stand for the right hand and left circular helicity respectively. e argue that in a Stern-Gerlach experiment (SGE) the magnetic moment is an important property but not the spin of the particles. Because of these two symmetric values of the magnetic moment, we expect a splitting of the gamma photon beam into two symmetric sub beams in a (SGE). We believe that the present result will be helpful for understanding the recent attempts on the (SGE) with slow light and the behavior of the dark polaritons and also the atomic spinor polaritons.