LIMITATIONS OF GAUGE INVARIANCE

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PHYSICAL <strong>GAUGE</strong> Electrostatics can be formulated self-consistently with scalar potentials alone. Any gauge transformation will preserve the particle trajectory, but will introduce some unphysical feature such as the failure of energy conservation. Implication: there exists a gauge that is entirely physical. For electrostatics, the physical gauge is the gauge with only a scalar potential and no vector potential. 0, A = 0 Static (and quasistatic) fields are called longitudinal fields. The electric field follows field lines from one plate of a parallel plate capacitor to the other. This can be viewed as the “propagation” of the electric field in a direction parallel to the polarization direction. Any gauge transformation from the physical gauge introduces some feature(s) that are nonphysical, even though gauge invariance holds true. 16
CAUTIONS ABOUT THE “PHYSICAL <strong>GAUGE</strong>” CONCEPT The concept is: every gauge transformation induces some alteration in physical interpretation; therefore, there can be only one gauge that matches laboratory conditions in every respect. This concept has been criticized on the grounds of an insufficiently precise definition of the “physical gauge”. So far, the debate has engaged only a small number of qualified people. The long-term outcome is still in doubt. Interim advice: unless you relish tough debates, avoid this concept for now. (Personally, I think it is a very useful idea, and I believe the issue was actually settled long ago: the physical gauge is the Coulomb gauge.) 17
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: NEWTONIAN MECHANICS DIFFERS FROM OT
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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