LIMITATIONS OF GAUGE INVARIANCE

More documents

Recommendations

Info

OUTLINE • Review the rules for gauges and gauge transformations. • Examine an elementary one-dimensional classical example to illustrate some of the problems to be explored. • Show how conservation conditions can be changed by gauge transformations. • Examine the essential differences between Newtonian mechanics and other formulations. • Examples from strong-field physics. (Many gauge transformation difficulties are exacerbated by strong fields.) • Exhibit an essential difference between the properties of classical and quantum gauge transformations. • Show how the above demonstration solves some essential long-standing dilemmas in the foundations of strong-field physics. • The above considerations infer the existence of a physical gauge. (This is still controversial and not essential.) • Revisit the statements from the Preamble. 4
ELECTROMAGNETIC POTENTIALS Electric fields E and magnetic fields B can be written in terms of scalar potentials vector potentials A through the connections (Gaussian units) When substituted into Maxwell’s equations, and with the Lorentz condition enforced in order to decouple the and A equations, the result is the wave equations where is a charge density and J is a current density. 5
Page 1 and 2: LIMITATIONS OF GAUGE INVARIANCE and
Page 3: Furthermore… There is another set
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 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

Create successful ePaper yourself

Delete template?

Save as template?