Implementation and validation of the relativistic transient absorption theory within the dipole approximation

A relativistic transient absorption theory is derived, implemented and validated within the dipole approximation based on the time-dependent Dirac equation. Time-dependent simulations have been performed using the Dirac equation and the Schr"odinger equation for the Hydrogen atom in two different attosecond transient absorption scenarios. These simulations validate the present relativistic theory. The presented work can be seen as a first step in the development of a more general relativistic attosecond transient absorption spectroscopy method for studying heavy atoms, but it also suggests the possibility of studying relativistic effects, such as Zitterbewegung, in the time domain.