Effective Potential for Uniform Magnetic Fields through Pauli Interaction

TL;DR

This paper derives the effective potential for uniform magnetic fields interacting with spin-1/2 fermions via Pauli interaction, revealing a critical field strength beyond which the field becomes unstable and produces fermion pairs.

Contribution

It provides an explicit calculation of the effective potential's real and imaginary parts for fermions with Pauli interaction in magnetic fields, highlighting the onset of instability.

Findings

Imaginary part appears above a critical magnetic field strength.

Field instability leads to fermion pair production.

Production rate depends on magnetic field and fermion properties.

Abstract

We have calculated the explicit form of the real and imaginary parts of the effective potential for uniform magnetic fields which interact with spin-1/2 fermions through the Pauli interaction. It is found that the non-vanishing imaginary part develops for a magnetic field stronger than a critical field, whose strength is the ratio of the fermion mass to its magnetic moment. This implies the instability of the uniform magnetic field beyond the critical field strength to produce fermion pairs with the production rate density $w(x)=\frac{m^{4}}{24\pi}(\frac{|\mu B|}{m}-1)^{3}(\frac{|\mu B|}{m}+3)$ in the presence of Pauli interaction.