Axion-electrodynamics: a quantum field calculation

Understand

An axion background field induces tiny oscillating electric and magnetic fields in an external static magnetic field.

• This signature is used to search for axion dark matter.
• We use standard quantum field theory techniques to obtain an expression for a transition amplitude, from which we identify the classical electromagnetic fields induced by the background axion field.
• We confirm previous results, that if the spatial size $R$ of the applied static magnetic field is small compared to the axion Compton wavelength $\lambda$, the induced electric and magnetic fields are parametrically suppressed by the small numbers $(R/\lambda)^2$ and $R/\lambda$, respectively, relative to the case when $R$ is larger than $\lambda$.