Inverse approach to solutions of the Dirac equation for space-time dependent fields

Abstract

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding non-perturbative phenomena in quantum electrodynamics (QED). However, for the limited set of known solutions, the field often depends on one coordinate only, which could be the time $t$, a spatial coordinate such as $x$ or $r$, or a light-cone coordinate such as $ct-x$. By swapping the roles of known and unknown quantities in the Dirac equation, we are able to generate families of solutions of the Dirac equation in the presence of genuinely space-time dependent electromagnetic fields in $1+1$ and $2+1$ dimensions.

7 pages, 2 figures

References in corpus (4)

• Dynamically assisted Schwinger mechanism
• Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory
• Pair production in laser fields oscillating in space and time
• Strong field effects in laser pulses: the Wigner formalism

Cited by in corpus (6)

• Advances in QED with intense background fields
• Classical and quantum particle dynamics in univariate background fields
• WKB approach to pair creation in spacetime-dependent fields
• Analytic Solutions to Coherent Control of the Dirac Equation
• Non-dispersive analytical solutions to the Dirac equation
• First and second-order relativistic corrections to the two and higher-dimensional isotropic harmonic oscillator obeying the spinless Salpeter equation