## Advanced Electromagnetism: Foundations, Theory and ApplicationsAdvanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met. |

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### Contents

Gauge Theories and Beyond | 3 |

Helicity and Electromagnetic Field Topology | 52 |

Einsteins | 77 |

The Symmetry Between Electricity and Magnetism | 105 |

Quantization as a Wave Effect | 148 |

Twisters in Field Theory | 182 |

Foundational Electrodynamics and Beltrami Vector Fields | 217 |

A Classical Field Theory Explanation of Photons | 250 |

A Consequence of Conservation of Action | 278 |

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algebra Ampere angular antenna armature axis beam Beltrami Broglie bundle classical complex components condition conservation laws constant coordinates corresponding covariant current density cylindrical defined derivative differential equations dipole current Dirac dyadic effect electric field electrodynamics electromagnetic field electron expression field equations field strength field theory formula frequency functions gauge theory geometry gravitation Green functions helicity Hopf invariant in-gap integral intensity interaction invariant laser Lett linear Lorentz force magnetic charge magnetic field magnetic monopole mathematical Maxwell Maxwell's equations mechanics Minkowski Minkowski space modes momentum monopole motion nonlinear obtained optical parameters particle periodic structure Phys physical polarization propagation pulse quantization quantum radiation radius railgun relation relativistic representation rotation Sagnac effect Sagnac interferometer scalar solitons solution space space-time spherical spinor Stokes theorem symmetry tensor theorem topological transformation twistor values variables vector field vector potential velocity wave equation wire zero