LIMITATIONS OF GAUGE INVARIANCE

INCORRECT PREDICTIONS FROM TUNNELING THEORY
• A laser field is strong when the electric field is of the order of one
atomic unit; that is, when the external field is of the order of magnitude
of internal fields in the atom. (Already examined.)
• A single parameter – the Keldysh parameter γ – is sufficient for scaling.
• Weak fields can be characterized as in the multiphoton domain and
strong fields are in the tunneling domain.
• A tunneling limit or classical limit will be approached at long
wavelengths of the field.
• There are no evident upper and lower frequency limits on the dipole
approximation.
• Higher harmonics are not produced by circularly polarized fields
because the photoelectron “walks away” from the atom.
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