LIMITATIONS OF GAUGE INVARIANCE

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PLANE WAVES A plane wave is a pure transverse field. The electric field vector is perpendicular to the propagation direction. A true plane wave has also a magnetic field B, equal in magnitude to the electric field E (Gaussian units) with both fields forming a mutually orthogonal triad with the propagation vector k. This is a vector field that requires a vector potential for its description. Long experience in quantum electrodynamics, quantum field theory, elementary particle physics,… has shown that the PHYSICAL <strong>GAUGE</strong> IS THE RADIATION <strong>GAUGE</strong>: = 0, A 0 18
MIXED FIELDS The physical gauge for a mixture of static and plane wave fields has been known for many years. It is the Coulomb gauge. For present purposes it can be defined as that gauge wherein static electric fields are represented by scalar potentials and plane wave fields are represented by vector potentials. For an atomic electron in a laser field: H 1 1 pˆ A 2 c 2 V in atomic units (ħ=m=|e|=1), where V(r) is the binding potential. In the dipole approximation, where A = A(t), this gauge is often called the velocity gauge. r 19
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: CAUTIONS ABOUT THE “PHYSICAL GAUG
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 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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