Asymptotic behavior of the effective charge in QED

We study the effective charge ${\mathrm{\alpha }}_{\mathrm{eff}}$ in QED as a function of a magnetic field B and chemical potential μ as each becomes large with the other held fixed. We find that ${\mathrm{\alpha }}_{\mathrm{eff}}$ grows at most logarithmically as B→∞, but there is a term which grows linearly in μ for fixed B, thereby leading to the possibility that ${\mathrm{\alpha }}_{\mathrm{eff}}$ becomes large in this limit.