Fermion Production in Strong Magnetic Field and its Astrophysical Implications

TL;DR

This paper investigates the instability of strong magnetic fields due to fermion pair production, revealing non-perturbative effects and potential astrophysical implications, especially in inhomogeneous magnetic environments.

Contribution

It provides explicit calculations of the effective potential for fermions with anomalous magnetic moments in strong magnetic fields, highlighting differences from the Schwinger process and analyzing inhomogeneous field effects.

Findings

Imaginary part of the effective potential appears above a critical magnetic field.

In inhomogeneous fields, pair production occurs even below the critical field.

The results suggest magnetic field instability leading to fermion pair creation.

Abstract

We calculate the effective potential of a strong magnetic field induced by fermions with anomalous magnetic moments which couple to the electromagnetic field in the form of the Pauli interaction. For a uniform magnetic field, we find the explicit form of the effective potential. It is found that the non-vanishing imaginary part develops for a magnetic field stronger than a critical field and has a quartic form which is quite different from the exponential form of the Schwinger process. We also consider a linear magnetic field configuration as an example of inhomogeneous magnetic fields. We find that the imaginary part of the effective potential is nonzero even below the critical field and shows an exponentially decreasing behavior with respect to the inverse of the magnetic field gradient, which is the non-perturbative characteristics analogous to the Schwinger process. These results imply the instability of the strong magnetic field to produce fermion pairs as a purely magnetic effect. The possible applications to the astrophysical phenomena with strong magnetic field are also discussed.