Instability of constant Yang-Mills fields

Abstract

Both a constant (non-Abelian) electric field and a constant magnetic field are solutions to the sourceless Yang-Mills field equations in Minkowski space. We discuss the stability of these solutions under small fluctuations in the potentials. We conclude that a magnetic field $B$, which is constant over a region of size $L$, has instabilities which grow exponentially in time provided $\mathrm{gB}{L}^{2}\ensuremath{\gtrsim}1$. A constant electric field is unstable. A fluctuation in such a field will accelerate continuously in the direction of the field.