LIMITATIONS OF GAUGE INVARIANCE

ANOTHER FUNDAMENTAL PROBLEM
The ponderomotive energy U p is a fundamental quantity in strong-field physics. (It
does not appear in any finite order of perturbation theory – but that is a different
interesting story.)
The ponderomotive energy can be such that
U
p
E
B
even within the domain where the dipole approximation is valid.
In atomic units,
U p
where the angle bracket means a time average over a full period. Within the dipole
approximation,
1
2
A
c
2
A A
2 ( t) U U ( t)
2
p
p
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