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.