LIMITATIONS OF GAUGE INVARIANCE

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EXPLANATION Because the frequency is high ( >> E B ), the ionization process takes place at low intensities with a single photon. In the SFA, the stabilization occurs because the ponderomotive energy has become so large as a result of increasing the field strength that the single-photon channel has closed and at least two photons are required for ionization. There are no channel closings in the HFA because A 2 (t) has been removed by a gauge transformation. The physical explanation for why stabilization has occurred has changed (there is no simple explanation in the HFA), but gauge equivalence preserves the physical effect. This is another example (beyond tunneling) where the physical explanation is dependent on the gauge even when gauge equivalence leads to the same predicted result. 52
REVISIT ITEMS FROM THE PREAMBLE • Physical processes involving electromagnetic interactions depend entirely on the electric and magnetic fields that are present. Physical processes depend on potentials as well as fields. See the first example of the constant electric field. • These fields can be represented as derivatives of scalar and vector potential functions that are often mathematically convenient, but are actually only auxiliary quantities. Potentials play a more fundamental role than just being “auxiliary quantities”. • The potential functions are not unique. There are many sets of these functions corresponding to the same fields and thus to the same physical processes. Different gauges can correspond to the same fields, but not to the same physical processes. The stabilization example is very clear on this point. 53
Page 1 and 2: LIMITATIONS OF GAUGE INVARIANCE and
Page 3 and 4: Furthermore… There is another set
Page 5 and 6: ELECTROMAGNETIC POTENTIALS Electric
Page 7 and 8: GAUGE TRANSFORMATION If is any sca
Page 9 and 10: THERE ARE HINTS OF BASIC PROBLEMS F
Page 11 and 12: These equations can be combined to
Page 13 and 14: GAUGE EQUIVALENT - BUT DIFFERENT Th
Page 15 and 16: NEWTONIAN MECHANICS DIFFERS FROM OT
Page 17 and 18: CAUTIONS ABOUT THE “PHYSICAL GAUG
Page 19 and 20: MIXED FIELDS The physical gauge for
Page 21 and 22: ATOMIC UNITS 1; m 1; e 1, or q 1 e
Page 23 and 24: V(r) LASER PHYSICS IN THE LENGTH GA
Page 25 and 26: Intensity (a.u.) Intensity (W/cm 2
Page 27 and 28: QUALITATIVE IMPLICATIONS OF THE VEL
Page 29 and 30: DOMAINS FOR AN ELECTRON IN A PLANE-
Page 31 and 32: VG-LG COMPARISON It has just been s
Page 33 and 34: CONTRADICTIONS Much success has bee
Page 35 and 36: PONDEROMOTIVE ENERGY A charged part
Page 41 and 42: ANOTHER FUNDAMENTAL PROBLEM The pon
Page 43 and 44: RIGOROUS DERIVATION OF AN S MATRIX
Page 45 and 46: By hypothesis, the laser pulse is f
Page 47 and 48: The end result of this alternative
Page 49 and 50: TRANSITION MATRIX ELEMENTS ARE NOT
Page 51: The SFA includes A 2 (t); the HFA h

LIMITATIONS OF GAUGE INVARIANCE

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