LIMITATIONS OF GAUGE INVARIANCE

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FOOTNOTES ABOUT THE LORENTZ CONDITION One of the senior participants in the Joint Theoretical Physics Colloquium expressed a dislike for the Lorentz condition. I disagree, based on its necessity for decoupling the inhomogeneous wave equations for scalar and vector potentials. Arguments based on approximations that relieve the necessity for strict adherence to the Lorentz condition become questionable when fields are strong. There is a superficial discrepancy in the LG, where A = 0 and /t 0, but this is not essential because there is no wave equation for A from which to decouple. However, the fact that /t 0 IS important because the wave equation for then requires a source density , whereas a plane wave does not require any sources. This just emphasizes the unphysical nature of the LG for description of PW phenomena. There is a separate issue with the Coulomb gauge. It is stated in many textbooks (including Jackson) that a defining condition for the Coulomb gauge is that A= 0. That condition, plus the constraint = 0 , leads to the Lorentz condition being satisfied. However, there is no covariant (completely relativistic) equivalent for this, whereas the Lorentz condition in its full form does have a covariant statement. 6
<strong>GAUGE</strong> TRANSFORMATION If is any scalar function that satisfies the homogeneous wave equation then the gauge transformation leaves the electric and magnetic fields unchanged. LORENTZ FORCE A particle of charge q, subjected to an electric field E and a magnetic field B while moving with velocity v will experience a force F Lorentz : 7
Page 1 and 2: LIMITATIONS OF GAUGE INVARIANCE and
Page 3 and 4: Furthermore… There is another set
Page 5: ELECTROMAGNETIC POTENTIALS Electric
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 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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