LIMITATIONS OF GAUGE INVARIANCE

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A FUNCTION <strong>OF</strong> TIME ONLY f(t), CAN BE REMOVED BY A <strong>GAUGE</strong> TRANSFORMATION This is not the same as simply dropping a function of time. A gauge transformation should, under appropriate conditions, make it possible to calculate laboratory measurables. The ponderomotive energy can be the cause of “channel closings”, and also the cause of “high-frequency stabilization”. These are physically important effects. A dilemma appears to remain. The simplest case to consider is the stabilization matter. “Stabilization” is that property of strong-field phenomena where, beyond a certain field intensity, further increases in intensity lead to a decline in the transition rate rather than an increase. The next figures [from HRR, J. Opt. Soc. Am. B 13, 355 (1996)] show the results of calculating with the SFA (Strong-Field Approximation) and the HFA (High Frequency Approximation). The stabilization occurs at about the same intensity with both methods, but A 2 (t) is included in the SFA, and it has been removed by a gauge transformation in the HFA. 50
The SFA includes A 2 (t); the HFA has removed that term by a gauge transformation. 51
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: TRANSITION MATRIX ELEMENTS ARE NOT
Page 53 and 54: REVISIT ITEMS FROM THE PREAMBLE •

LIMITATIONS OF GAUGE INVARIANCE

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