LIMITATIONS OF GAUGE INVARIANCE

STRONG-FIELD LASER PHYSICS
As laser capabilities have mushroomed in recent years, strong-field laser
physics has become a field with large numbers of participants.
The field is characterized by the near-universal realization that
perturbation theory does not work; and by near-universal
misconceptions about gauges.
From a theory standpoint, there are 3 distinct approaches:
• Direct numerical solution of the Schrödinger equation.
• Analytical approximations in the length gauge.
• Analytical approximations in the velocity gauge.
With a few exceptions (significant but largely unexploited), all
theoretical work is nonrelativistic and in the dipole approximation.
Atomic units are used almost universally.
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