Landau levels of scalar QED in time-dependent magnetic fields

•We study the Landau levels of scalar QED in time-dependent magnetic fields.•Instantaneous Landau levels make continuous transitions but keep parity.•The Klein–Gordon equation is expressed in the two-component first order formalism.•A measure is advanced that characterizes the quantum motions into three categories.•A suddenly changing magnetic field produces pairs of charged scalars from vacuum.

The Landau levels of scalar QED undergo continuous transitions under a homogeneous, time-dependent magnetic field. We analytically formulate the Klein–Gordon equation for a charged spinless scalar as a Cauchy initial value problem in the two-component first order formalism and then put forth a measure that classifies the quantum motions into the adiabatic change, the nonadiabatic change, and the sudden change. We find the exact quantum motion and calculate the pair-production rate when the magnetic field suddenly changes as a step function.