Spin and Statistics with an Electromagnetic Field

Abstract

Because of the impossibility of simultaneously satisfying the requirements of manifest Lorentz covariance and positive‐definite (finite) norm in the Hilbert space, no simple proof of the connection between spin and statistics with an electromagnetic field has been given. This note is to point out that it is indeed not necessary to have manifest Lorentz covariance in the full 3 + 1 space to show such a connection. Using the axial gauge A₃ = 0, we have succeeded in constructing a simple straightforward proof.