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Abstract

Tunnel-ionization is investigated in the framework of relativistic quantum mechanics. For an arbitrary constant electromagnetic field a gauge invariant energy operator is introduced in order to identify the classically forbidden region for tunnel-ionization. Furthermore, relativistic features of tunnel-ionization are explored. A one-dimensional intuitive picture predicts that the ionized electron wave packet in the relativistic regime experiences a momentum shift along the laser’s propagation direction. This is shown to be consistent with the well-known strong field approximation. Furthermore, spin dynamics in tunnel-ionization process is discussed in the standard as well as in the dressed strong field approximation. Next, the tunneling time delay is investigated for tunnel-ionization by extending the definition of the Wigner time delay. Later, this concept is redefined in terms of the phase of the fixed energy propagator. The developed formalism is applied to the deep-tunneling and the near-threshold-tunneling regimes. It is shown that in the latter case signatures of the tunneling time delay can be measurable at remote distance. Finally, the path-dependent formulation of gauge theory is discussed. It is demonstrated that this equivalent formulation of gauge theory leads to a canonical gauge fixing, in which the Feynman path integral becomes more intuitive and the calculation of the quasiclassical propagator is considerably simplified.