| Preface | p. vii |
| Introduction | p. 1 |
| Interaction of Electromagnetic Radiation with One Fermion | p. 3 |
| Lorentz Electron | p. 3 |
| Radiation Induced Electron and Proton Spin Rosonance | p. 8 |
| The B[superscript (3)] Field | p. 10 |
| Electrodynamics as a NonAbelian Gauge Field Theory | p. 10 |
| Limitations of the U(1) Theory | p. 13 |
| Classical Relativistic NonAbelian Electrodynamics | p. 20 |
| Relativistic Quantum Description | p. 23 |
| Nonrelativistic Quantum Description | p. 24 |
| Schrodinger Equation with Intrinsic Spin | p. 26 |
| Resonance Conditions in RFR | p. 28 |
| Chemical Shifts in NMR | p. 30 |
| Classical Derivation of the Inverse Faraday Effect | p. 32 |
| References | p. 34 |
| The Field Equations of Classical O(3)[subscript b] Electrodynamics | p. 37 |
| Introduction | p. 37 |
| The O(3)[subscript b] Field Equations | p. 37 |
| Basic S. I. Units | p. 38 |
| The O(3)[subscript b] Vacuum Equations | p. 39 |
| The Coefficient g in the Vacuum | p. 39 |
| The O(3)[subscript b] Field Tensor in the Vacuum | p. 41 |
| Reduction to Maxwell's Equations | p. 47 |
| The Fundamental Laws of O(3)[subscript b] Electrodynamics | p. 51 |
| The Lorentz Force Equation in O(3)[subscript b] Electrodynamics | p. 54 |
| Continuity Equation and Lorentz Condition in O(3)[subscript b] Electrodynamics | p. 56 |
| Primitive Concepts, Axioms and Constitutive Relations of O(3)[subscript b] Electrodynamics | p. 57 |
| The Inverse Faraday Effect | p. 60 |
| The effective A[superscript (3)] Potential, Photoelectric and Compton Effects and Radiation Reaction | p. 67 |
| Summary | p. 73 |
| References | p. 74 |
| Origin of Electrodynamics in the General Theory of Gauge Fields | p. 77 |
| Closed Loop in Minkowski Space | p. 77 |
| Gauge Transformations | p. 80 |
| Gauge Transformation in the O(3)[subscript b] Group | p. 84 |
| The Sagnac Effect | p. 86 |
| Observation of B[superscript (3)] in the Topological Phase | p. 92 |
| The NonAbelian Stokes Theorem and the Electromagnetic Phase | p. 102 |
| Link between B Cyclic Theorem and the NonAbelian Stokes Theorem | p. 109 |
| References | p. 111 |
| Nonlinear Propagation in O(3)[subscript b] Electrodynamics: Solitons and Instantons | p. 115 |
| Limitation in the U(1) Theory | p. 115 |
| Identification of the Harmuth and O(3)[subscript b] Field Equations | p. 116 |
| Structure of the O(3)[subscript b] and Harmuth-Barrett Field Equations | p. 118 |
| Link between the O(3)[subscript b] Equations and the Sine-Gordon Equations | p. 122 |
| Instantons | p. 127 |
| Higher Order Soliton Equations | p. 132 |
| References | p. 136 |
| Physical Phase Effects in O(3)[subscript b] Electrodynamics | p. 137 |
| Phase Effects | p. 137 |
| The Optical Ahronov-Bohm Effects | p. 147 |
| Phase Shift of the Inverse Faraday Effect | p. 152 |
| Phase Shift of the Optical Josephson Effect | p. 155 |
| Phase Factor of the Optical Hall Effect | p. 156 |
| References | p. 156 |
| Quantum Electrodynamics and the B[superscript (3)] Field | p. 159 |
| Introduction to Quantum Electrodynamics | p. 159 |
| A Brief Introduction to Differential Forms | p. 168 |
| The Physical Basis for NonAbelian Electrodynamics | p. 170 |
| The Quantized U(1) and O(3)[subscript b] Electrodynamic Field | p. 179 |
| Numerical Results | p. 182 |
| Discussion of these Results | p. 204 |
| Quantum Electrodynamics of Elementary Scattering | p. 206 |
| Physics of Quantum Electrodynamics of Electrons and Photons with the B[superscript (3)] Field | p. 212 |
| Nonrelativistic Estimate of the B[superscript (3)] Contribution to the Lamb Shift | p. 217 |
| Derivation of the 1/f Spectrum from NonAbelian Electrodynamics | p. 222 |
| Analogy from Classical Field to NonAbelian Quantum Electrodynamics | p. 227 |
| References | p. 234 |
| Quantum Chaos, Topological Indices and Gauge Theories | p. 237 |
| Introduction | p. 237 |
| Topological Number and Quantum Vortices | p. 238 |
| Density Operator Methods | p. 241 |
| Hamiltonian Chaotic Systems | p. 246 |
| Quantum Geometry and Bohm's Theory | p. 248 |
| Discussion and Problems | p. 257 |
| References | p. 259 |
| Field Theory of O(3)[subscript b] QED and Unification with Weak and Nuclear Interactions | p. 261 |
| Discussion | p. 261 |
| Basics of Relativistic O(3)[subscript b] QED | p. 262 |
| Renormalization of O(3)[subscript b] QED | p. 275 |
| B[superscript (3)] Field as a Vacuum Symmetry | p. 282 |
| SU(2) x SU(2) Electroweak Theory with One Higgs Field | p. 285 |
| The SU(2) x SU(2) Extended Standard Model | p. 286 |
| Duality and Chiral Breaking | p. 293 |
| Discussion of the Theory, its Problems and their Remedies | p. 294 |
| Chiral and Vector Field in SU(2) x SU(2) Electroweak Field | p. 296 |
| Axial-Vector SU(2) x SU(2) Fields: A First Look | p. 297 |
| Chiral and Vector Gauge Theories from Chiral Gauge Theories on the Physical Vacuum | p. 301 |
| The Occurrence of O(3)[subscript b] Electrodynamics on the Physical Vacuum | p. 304 |
| The SU(4) Model | p. 305 |
| Duality in Grand Unified Field Theory, and Recent LEP1 Data | p. 306 |
| References | p. 310 |
| Potential Application of O(3)[subscript b] QED | p. 313 |
| Computation, Biophysics and B[superscript (3)] Induced Entangled States | p. 313 |
| B[superscript (3)] Field and the Sequencing of DNA | p. 330 |
| Duality and Fundamental Problems | p. 339 |
| Foundations for SU(2) Electromagnetism | p. 339 |
| Rotations between Spacetime Conjugate Variables and Their Fluctuations in Quantum Gravity | p. 343 |
| Duality: Questions, Numerical Probes, and Quantum Uncertainty | p. 353 |
| Gravitation with One Killing Isometry | p. 371 |
| Brief Discussion on String Theory | p. 381 |
| Map between the String Surfaces and the Spacial 2-Surface | p. 403 |
| Overview of Conformal Groups | p. 414 |
| Conformal Structure of the Vacuum | p. 420 |
| Conformal Group and Gauge Theories According to Weighted Projective Spaces | p. 425 |
| Conformal Theory of W[infinity] String Vortices | p. 431 |
| Concluding Statements on Duality | p. 434 |
| References | p. 437 |
| Applications of Stokes' Theorem | p. 441 |
| Bianchi IX Cosmologies | p. 444 |
| References | p. 445 |
| Index | p. 447 |
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