LIMITATIONS OF GAUGE INVARIANCE

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PROBLEMS ASSOCIATED WITH THE KELDYSH PARAMETER If the binding energy is set at E B = 0.5 a.u. (ground-state hydrogen), then I ( / ) 2 Plotted as I vs. , this produces the following simple diagram that completely contradicts the “standard tunneling / multiphoton” classification. 36
Intensity (a.u.) Intensity (W/cm 2 ) 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 Wavelength (nm) 10 4 10 3 10 2 10 1 10.6 m CO 2 E=1a.u. 800 nm Ti:sapph = 0.1 = 1.0 = 10 10 -3 10 -2 10 -1 10 0 10 1 Field frequency (a.u.) 100 eV 10 23 10 22 10 21 10 20 10 19 10 18 10 17 10 16 10 15 10 14 10 13 A fixed value of cannot distinguish “tunneling” from “multiphoton”. = 0.1 is supposedly “tunneling”, but the right-hand end of this line is at 10 a.u. = 272 eV. 37
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: PONDEROMOTIVE ENERGY A charged part
Page 39 and 40: Intensity (a.u.) Intensity (W/cm 2
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 and 52: The SFA includes A 2 (t); the HFA h
Page 53 and 54: REVISIT ITEMS FROM THE PREAMBLE •

LIMITATIONS OF GAUGE INVARIANCE

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