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O(3) invariance, 169–170 quantum light theory: Aharonov-Bohm effect, O(3) electrodynamics, 80–87 gauge theory development in vacuum, 52–62 Proca equation, 12–21 767 Kaluz-Klein model, light velocity, constancy of, lightcone fluctuation, 590–593 k-deformed quantum relativistic phase space, light velocity, constancy of, 593–596 Kinetic electromagnetic energy, quantum light theory, Aharonov-Bohm effect, 158–163 Kinetic phase transition, optically bistable (OB) systems, fluctuational transitions, 479 Klein-Gordon equation: light velocity, constancy of, nonzero photon mass, 607–610 quantum light theory: Proca equation, 8–21 Schro¨ dinger equation, Higgs mechanism with, 63–68 single-particle quantization, 68–74 Koldamasov low-energy nuclear reactor, highdensity charge clusters, 647 Korteweg de Vries soliton equation, topological model of electromagnentism, 701 soliton particles, 709–711 Kramers’ relation: optically bistable (OB) systems, fluctuational transitions, 479 optimal paths, fluctuation escapes, 495–497 Kundt tube, sound velocity measurement, 389 Lagrangian equations: Beltrami vector fields, spinor-Hertz potential connection, 554–561 electromagnetic topology, 230–232 Faraday and Ampe`re-Maxwell laws, O(3) and SU(3) invariance, 143–148 Mach’s principle: equations of motion, 325–326 time-dependent expressions, 323–324 non-Abelian electrodynamics: chiral/vector gauge theory, chiral twisted bundle, 417–419 duality in grand unified theory, 423 SU(4) gauge theory, 420 SU(2) x SU(2) extended standard model, 406–411 quantum electrodynamics (QED), relativistic theory, 440–449 quantum light theory: Aharonov-Bohm effect, 150–163 Lehnert-Proca vacuum charge current density, 22–48 768 subject index Lagrangian equations: (Continued) Schro¨ dinger equation, Higgs mechanism with, 63–68 single-particle quantization, 68–74 Lagrangian manifold (LM), optimal paths, fluctuation escapes, 489–491, 495–497 Lamb shift, O(3) electrodynamics, irreducible representations, 173–176 Landau gauge, quantum electrodynamics (QED), relativistic theory, 447–449 Landau-Ginzburg free energy: Beltrami vector fields, FFMF topology, superconductivity, 541–542 quantum light theory, gauge theory development in vacuum, 55–62 Laplace equation: quantum light theory, B cyclic theorem quantization, 133–142 sound velocity, 388–389 Lax pairs, topological model of electromagnentism, soliton particles, 708–711 Leaky evanescent waves, superluminal relativity theory (SLRT), photon tunneling evanescent waves, 690–692 Least-arbitrariness principle, Michelson-Morley interferometry, 393–394 Legendre polynomials, quantum light theory, B cyclic theorem quantization, 132–142 Lehnert equation: Faraday and Ampe`re-Maxwell laws, O(3) and SU(3) invariance, 144–148 O(3) electrodynamics, irreducible representations, 171–176 quantum light theory: Aharonov-Bohm effect, 163 gauge theory development in vacuum, 56–62 O(3) electrodynamics charge current densities, 74–77 Proca equation, 18–21 Lehnert-Proca vacuum charge current density, quantum light theory, 22–48 LEP collaboration, quantum light theory: gauge theory development in vacuum, 60–62 Proca equation, 11–21 LEP1 data, non-Abelian electrodynamics, duality in, 421–423 Levi-Civita symbol: Beltrami vector fields, spinor-Hertz potential connection, 558–561 O(3) electrodynamics, self-consistent calculations, complex circular algebra, 117–122 quantum light theory, B cyclic theorem quantization, 122–142 Lie algebra: electromagnetic knots, Hopf fibration, 221–223 non-Abelian electrodynamics: SO(10) grand unification model, 458–463 SU(2) x SU(2) extended standard model, 408–411 O(3) electrodynamics: irreducible representations, 172–176 self-consistent calculations, complex circular algebra, 121–122 quantum electrodynamics (QED): non-Abelian principles, 432–436 relativistic theory, 443–449 quantum light theory: B cyclic theorem quantization, 123–142 Proca equation, 16–21 topological model of electromagnentism, 700–707 Liener-Wiechert potentials, hidden nonlinearity, 241–242 Lightcones: light velocity, constancy of: fluctuations and, 590–593 parallel branes, 592–593 Minkowski intersections, 257–260 Light-in-flight (LIF) recording, holography: holodiagram applications, 260–262 orthogonal coordinate transformation, 285–286 techniques, 266–268 Light propagation: geometric optics, 388 incompleteness of light theory, 399 research background, 387–388 superluminal relativity theory (SLRT): anomalous dispersion media, 691–693 Wang-Kuzmich-Dogaru (WKD) effects, 678–680 Light spheres paradox, holography and special relativity, 272–274 Light velocity, constancy of: subject index cosmological photon propagation and expansion, 588–590 energy-dependent speed of light, 596–601 gamma-ray bursteres (GRB), 574–582 k-deformed quantum relativistic phase space, 593–596 lightcone fluctuations, 590–593 Maxwell vacuum nonzero conductivity, 596–601 nonzero photon mass, 604–607 longitudinal solutions, 607–610 photon pulse propagation, space-time foam, 586–588 quantum gravity effects, 584–586 research background, 571–574 stochastic background, 610–618 applications and results, 615–618 moments and metrics, 614–615 in vacuo space charges, 601–604 Linear equations, electromagnetic knots, 201 Linear response theory (LRT), nonlinear optics, fluctuational escape, research background, 472–476 Lissajous patterns, topological model of electromagnetism, polarization modulation, 721–723 Local equivalence, electromagnetic knots, 236–240 Local gauge transformation, quantum light theory, Aharonov-Bohm effect, 160–163 Localized diffraction, superluminal relativity theory (SLRT), 693–695 Logarithmic susceptibility, nonlinear optics, fluctuational escape, 475–476, 497–500 London equations, Beltrami vector fields, FFMF topology, 541–542 Longitudinal current density, quantum light theory, Lehnert-Proca vacuum charge current density, 34–48 Longitudinal magnetic fields: Beltrami vectors, B(3) longitudinal field, 561– 562 light velocity, constancy of, nonzero photon mass, 607–610 semiclassical photon models, Maxwell’s freespace equations, 353–357 Lorentz electron theory, semiclassical photon models, Maxwell’s free-space equations, equivalence with, 352 769 Lorentz force law, topological models of electromagnetism, Aharonov-Bohm effect, 728–733 Lorentz-Poincare´ field invariants, Beltrami vector fields: future reserach, 564–565 Rodrigues-Vaz model, 560–561 Lorentz transformation: Beltrami vector fields: force-free magnetic fields (FFMFs) hypothesis, 537–539 Rodrigues-Vaz model, 557–561 charge-neutral/mass-neutral photon models, rotating doublet, electrostatic force, 373–376 electromagnetic helicity, 211 electromagnetic topology model, 233–236 light velocity, constancy of: gamma-ray bursters (GRB), 575–582 quantum gravity effects, 584–586 Michelson-Morley interferometry, 394–395 particle meaning of helicity, 216–220 quantum electrodynamics (QED), relativistic theory, 440–449 quantum light theory: Aharonov-Bohm effect, O(3) electrodynamics, 81–87 B cyclic theorem, 122–142 B(3) field debate, 89 Proca equation, 17–21 Sagnac experiments, special relativity and, 398–399 semiclassical photon models, fourdimensional ether model, 364 special relativity, 256–257 graphical calculations, 275–278 Michelson-Morely interferometry, 268–270 orthogonal coordinate transformation, 284–286 time dilation and, 274–275 superluminal relativity theory (SLRT): principles of, 659–660 special relativity theory and, 656–658 X wave properties, 695 Lorenz attractor, quasihyperbolic fluctuational escape, 513–517 Lorenz-invariant inductive phenomena, light velocity, constancy of, nonzero photon mass, inverse effect, 610 770 subject index Low-energy nuclear reactions, high-density charge clusters, 646 Koldamasov low-energy nuclear reactor, 647 Lyapunov function: chaotic escape, optimal control, nonhyperbolic attractor, 503–513 optimal paths, fluctuation escapes, 489–491 Mach’s principle: alternative theories, 316 conventional theories, 315–316 cosmological potential, 327–328 discrete dynamical states research, 332 discrete model universe, 317–318 arbitrary displacements, absolute magnitudes, 319–321 dynamical constraints, 324 mass model, 319 radial coordinate, invariant calibration, 318–319 empty inertial spatiotemporal continuum, 313–314 equations of motion, 325–326 fractal D ¼ 2 inertial universe, 329–330 geodesic distance, matter distribution, 322–323 gravitational trajectories, 324–325 historical background, 312–313 metric tensor, mass model terms, 321–322 nonrelativistic formalism, 314 physical time, quantitative definition, 326–327 potential function, properties of, 328–329 qualitative approach, 316–317 quasifractal mass distribution law, 330–331 relativistic formalism, 314–315 spiral galaxies, discrete state phenomenon, 311–312 temporal dimension, qualitative analysis, 323–324 Mach-Zender effects, O(3) electrodynamics, phase factor development, 98–103 Magnetic charge, topological quantization, 243–249 Magnetic field solutions, force-free magnetic field (FFMF) equationsw, 544–547 Magnetic helicity: electromagnetic topology, 208 Maxwell’s theory in vacuum, 215–216 meaning of: force line topology, 211–214 Maxwell’s theory in vacuum, 214–216 particle meaning of, 216–220 research background, 210–211 Magnetic moments, superluminal dynamics, nuclear structures, 662–663 Magnetic tube, force line helicity and topology, 211–214 Magnus force-free flow, Beltrami vector fields, hydrodynamics, 527–528 Magnus pressure force, Beltrami vector fields, 530–531 Majorana equations, Faraday and Ampe`reMaxwell laws, O(3) and SU(3) invariance, 143–148 Markov systems, nonlinear optics, fluctuational escape, logarithmic susceptibility, 498–500 Mass model, radial coordinates, Mach’s principle, 319 displacement measurements, 319–321 metric tensor, 321–322 Mathewson-Ford-Buchhorn (MFB) sample, rotation curve measurement: Persic-Salucci eyeball method, 306–307 Roscoe automatic method, 307–308 Tully-Fisher relationship, 305–306 Mathewson-Ford (MF) sample, rotation curve measurement, Roscoe automatic method, 307–308 Matter distribution, Mach’s principle, radial displacement, geodesic distance, 322–323 Maxwell-Heaviside theory: Faraday and Ampe`re-Maxwell laws, O(3) and SU(3) invariance, 146–148 O(3) electrodynamics: irreducible representations, 171–176 phase factor development, 97–103 quantum light theory: Aharonov-Bohm effect, O(3) electrodynamics, 79–87 Lehnert-Proca vacuum charge current density, 24–48 Proca equation, 7–21 Maxwell’s equations: Beltrami vector fields: Rodrigues-Vaz model, 559–561 spinor-Hertz potential connection, 552–561 subject index time-harmonic electromagnetism in chiral media, 549 transverse electromagnetism (TEM), standing waves, 550–552 Trkalian field solutions, 547–549 charge-neutral/mass-neutral photon models, extended equations, 377–379 electromagnetic helicity, 214–216 electromagnetic knots, 201 global difference, 240 local equivalence, 236–240 vacuum equations, 220–229 electromagnetic topology model, hidden nonlinearity, 240–242 empty space equations: electromagnetic topology, 230–232 Faraday force lines, 202–206 magnetic/electric helicities, 208 ether properties, 389–390 light velocity, constancy of: quantum gravity effects, 584–586 research background, 573–574 in vacuo space charges, 601–604 vacuum, nonzero conductivity, 596–601 Michelson-Morley experiment and, 394–395 non-Abelian electrodynamics, 404 chiral and vector electroweak fields, 413 SU(2) x SU(2) extended standard model, 411 quantum electrodynamics (QED): basic principles, 424–430 non-Abelian principles, 433–436 quantum light theory, B cyclic theorem quantization, 138–142 Sagnac experiments, special relativity and, 398–399 semiclassical photon models: free space equations, 345–359 current density, 349–350 electromagnetic field, 347–349 ether, 345–347 longitudinal magnetic field components, 353–357 symmetrization, 357–359 wave equations and equivalence of, 350–352 vacuum electromagnetic energy, 339–340 superluminal dynamics, 656–658 771 topological models of electromagnetism: Aharonov-Bohm effect, 729–733 soliton particles, nonlinear form, 710–711 U(1) algebra, 706–707 Maxwell vector potential, quantum light theory: gauge theory development in vacuum, 50–62 Lehnert-Proca vacuum charge current density, 37–48 Mercury, perihelion precession, holographic ellipsoids, 294 Mesons, superluminal dynamics, 663 Metric space, light velocity, constancy of: quantum gravity effects, 584–586 stochastic background, 611–618 Metric tensor, mass model, Mach’s principle, 321–322 Michelson-Gale experiments, earth’s rotation measurements, 391–393 Michelson interferometry: Faraday and Ampe`re-Maxwell laws, O(3) and SU(3) invariance, 145–148 O(3) electrodynamics: Aharonov-Bohm effect, 86–87 phase factor development, 92–103 quantum light theory, Aharonov-Bohm effect, 157–163 Michelson-Morley interferometry: classical mechanics, 390–391 earth’s orbital velocity, 390–391 holography and, 268–270 incompleteness of light theory and, 399 Sagnac effect, 389–391 Einstein interpretation, 395 least-arbitrariness principle, 393–394 Lorentz interpretation, 394–395 special relativity and, 397–399 standing-wave interferometry, 395–396 semiclassical photon models, empirical verification, 342–345 time dilation, 256–257 Microwave propagation, superluminal relativity theory (SLRT), photon tunneling evanescent waves, 689–691 Migration control, chaotic oscillators, nonhyperbolic attractors, 511–513 Mikhailov effect, topological models of electromagnetism, instantons, 711 Mills energy device, high-density charge clusters, 648 Minkowski lightcone, intersections, 257–260 772 subject index Minkowski spacetime: electromagnetic helicity, Maxwell’s theory in vacuum, 214–216 electromagnetic topology model, 235–236 light velocity, constancy of, k-deformed quantum relativistic phase space, 594–596 O(3) electrodynamics: electromagnetism-general relativity link, 109–111 phase factor, 89–103 quantum light theory: Aharonov-Bohm effect, O(3) electrodynamics, 83–87 gauge theory development in vacuum, 48–62 Lehnert-Proca vacuum charge current density, 22–48 Proca equation, 13–21 superluminal relativity theory (SLRT), X wave properties, 695 Mirror reflection, holography, interferometric applications, 263–266 MKS system, topological models, 201–202 Moire´ effect, holographic ellipsoids, holodiagram calculations, 290–294 Monge decomposition, Beltrami vector fields, 532–533 Monte Carlo simulation, cosmological redshift quantization, Napier theory, 301–303 Moses curl, Beltrami vector fields, 563–565 Most probable escape path (MPEP), optimal paths, fluctuation escapes2, 496–497 Motion equations: Galilean transformation, 388 Mach’s principle: cosmological potential, 327–328 physical time, 326–327 relativity theory, 325–326 semiclassical photon models, fourdimensional ether model, 359–362 Motionless electromagnetic generator (MEG), high-density charge clusters, 649 Multipole radiation, quantum light theory, B cyclic theorem quantization, 132–142 Muons, superluminal dynamics, 663 Napier theory, cosmological redshift quantization, 301–303 Navier-Stokes equations, Beltrami vector fields: complex helical wave decomposition, 535 fluid turbulence, 533 theoretical principles, 532–533 Neutrinos: charge-neutral/mass-neutral photon models, 367–368 as tachyons, 686 Newtonian mechanics: earth’s motion and, 390 Faraday and Ampe`re-Maxwell laws, O(3) and SU(3) invariance, 146–148 geometric optics, 388 quantum light theory: Schro¨ dinger equation, Higgs mechanism with, 67–68 single-particle quantization, 70–74 Sagnac experiments, special relativity and, 398–399 semiclassical photon models, Maxwell’s freespace equations, 350 topological models of electromagnetism, soliton particles, 707–711 Newtonian physics: Michelson-Morley experiment and, 394–395 space-time properties, 388 Newton vacuum, quantum light theory, Schro¨ dinger equation, Higgs mechanism with, 66–68 Noether charges and currents, quantum light theory, Proca equation, 19–21 Noether’s theorem: quantum light theory: Aharonov-Bohm effect, 150–163 Lehnert-Proca vacuum charge current density, 25–48 topological model of electromagnentism, 701–702 soliton particles, 707–711 Noise-enhanced heterodyning, fluctuational escape, nonlinear optics, 484–486 Noise-protected heterodyning, nonlinear optics, fluctuational escape: noise-enhanced optical heterodyning, 484–486 optically bistable (OB) SR, 482–484 fluctuations and transitions, 477–482 research background, 476–477 Non-Abelian electrodynamics: Beltrami vector fields, spinor-Hertz potential connection, 556–561 subject index B(3) field research, future issues, 466–467 chiral and vector gauge theory, 417–419 cosomological applications, 463–466 current research problems, 412–413 grand unified field theory, duality and LEP1 data, 420–423 O(3) electrodynamics on physical vacuum, 419–420 quantum electrodynamics and, 423–463 B(3) field as vacuum symmetry, 455–458 physical principles, 431–436 quantized U(1)-O(3)b field, 437–440 relativistic O(3)b QED, 440–449 renormalization of O(3)b QED, 449–455 SO(10) grand unification, 458–463 research background, 403–406 SU(4) model, 420 SU(2) x SU(2) extended standard model, 406–411 axial vector in, 413–417 chiral and vector electroweak fields, 413 Non-Abelian Stokes theorem: O(3) electrodynamics: electromagnetism-general relativity link, 109–111 irreducible representations, 173–176 phase factor, 89–103 self-consistent calculations, complex circular algebra, 115–122 quantum light theory: Aharonov-Bohm effect, 154–163 Aharonov-Bohm effect, O(3) electrodynamics, 77–87 gauge theory development in vacuum, 50–62 Nonacceleration, Mach principle, inertial frames, 316 Nonequilibrium systems, nonlinear optics, fluctuational escape, 473–476 Nonhyperbolic attractor, chaotic escape, optimal control, 501–513 boundary value problem solution, 510–511 energy-optimal migration control, 511–513 fluctuation trajectories, statistical analysis, 506–510 Nonlinear optics, fluctuational escape: chaotic escape and optimal control problems, 500–517 nonhyperbolic attractor, 501–513 773 quasihyperbolic attractor, 513–517 logarithmic susceptibility, 497–500 optimal paths, fluctuations and irreversibility, 486–497 research background, 470–476 stochastic resonance and noise-protected heterodyning: noise-enhanced optical heterodyning, 484–486 optically bistable (OB) system, 477–484 research background, 476–477 Nonlinear Schro¨ dinger equation, topological model of electromagnentism, soliton particles, nonlinear form, 709–711 Nonrelativistic kinetic energy: Mach principle, 314 quantum light theory, Schro¨ dinger equation, Higgs mechanism with, 64–68 Nonzero conductivity, light velocity, constancy of, Maxwell vacuum and energydependent speed of light, 596–601 Nonzero photonic mass: light velocity, constancy of, longitudinal solutions, 607–610 principles of, 337–338 Nuclear fine-structure constraint, superluminal relativity theory, 669–670 Nuclear structures, superluminal dynamics, 662–663 Nuclear surface, superluminal relativity theory, 669–670 Nuclear transmutation, high-density charge clusters, 641–644 Nucleon structures, spacetime curvature, 664–676 general relativity, 664–665 light deflection equations, proton applications, 670–676 quantum gravity, 665–667 superluminal energy levels, 668–670 Null-field behavior: Beltrami vector fields, 557–561 topological models of electromagnetism, polarization modulation, 716–721 Observation spheres: holographic ellipsoids: future applications, 287 graphical calculations, 275–278 holodiagram calculations, 290–294 774 subject index Observation spheres: (Continued) observation ellipsoids, transformation into, 271–272 time dilation and Lorentz contraction, 274– 275 light spheres paradox, 272–274 Occam’s razor.

Edited by Myron W. Evans. Series Editors: I. Prigogine and Stuart A. Rice. Copyright # 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38932-3 (Hardback); 0-471-23149-5 (Electronic) THE PRESENT STATUS OF THE QUANTUM THEORY OF LIGHT M. W. EVANS AND S. JEFFERS Department of Physics and Astronomy, York University, Toronto, Ontario, Canada CONTENTS I. Introduction II. The Proca Equation III. Classical Lehnert and Proca Vacuum Charge Current Density IV. Development of Gauge Theory in the Vacuum V. Schro¨dinger Equation with a Higgs Mechanism: Effect on the Wave Functions VI.

Vigier Technical Appendix A: Criticisms of the U(1) Invariant Theory of the Aharonov–Bohm Effect and Advantages of an O(3) Invariant Theory Technical Appendix B: O(3) Electrodynamics from the Irreducible Representations of the Einstein Group References Publications of Professor Jean-Pierre Vigier 1 2 m. w. evans and s. jeffers I. INTRODUCTION If one takes as the birth of the quantum theory of light, the publication of Planck’s famous paper solving the difficulties inherent in the blackbody spectrum [1], then we are currently marking its centenary.