LIMITATIONS OF GAUGE INVARIANCE

DOMAINS FOR AN ELECTRON IN A PLANE-WAVE FIELD
Lasers produce plane-wave (PW) fields, not quasistatic (QSE) fields, so
the beyond-dipole-approximation results in the VG have significance
that the LG does not have.
Specifically, the limits of relativistic effects and magnetic field effects
shown on the next slide have real laboratory significance.
Also shown is the upper limit on intensity for which perturbation theory
is applicable. This follows from both a relativistic investigation [HRR, J.
Math. Phys. 3, 387 (1962)] and a nonrelativistic investigation [HRR, Phys.
Rev. A 22, 1786 (1980)].
Most of what follows here was a surprise for the Joint Theoretical Physics Colloquium, including
intensity-dependent failure of the dipole approximation.
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