## 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 |

Twistors 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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### Common terms and phrases

algebra antenna applied approximation associated beam bundle called charge classical closed complex components condition connection conservation consider constant coordinates corresponding defined density depends derivative described differential dipole direction discussed effect electric electrodynamics electromagnetic field electron element energy equal equations equivalent exact example existence experiment expression fact follows force formula frame frequency functions gauge given gives integral intensity interaction interpretation invariant light linear Lorentz magnetic field mass Maxwell Maxwell's measured mechanics modes momentum monopole motion observed obtained operator particle phase Phys physical polarization positive potential present problem produced quantum quantum mechanics radiation relation relativity representation represents requires respect rotation shown shows solution space space-time special relativity spinor structure surface symmetry tensor theorem theory transformation twistor values vector velocity wave wire zero