The aims of the book are: (1) to extend Maxwell theory to non-Abelian group forms; (2) to demonstrate that the foundations of electromagnetism are topological; (3) to show the multi-disciplinary nature of communications; (4) to demonstrate the effectiveness of modulated signals in penetrating media; (5) to demonstrate that geometric (Clifford) algebra is the appropriate algebra describing modulated signals.The book is important in indicating that the classical theory of electromagnetism, or Maxwell theory, can be developed to address situations and signals of differing symmetry form, and that different topological spaces require that development.

Advanced 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.

This self-contained text describes the underlying theory and approximate quantum models of real nanodevices for nanotechnology applications.

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.

An amazing book on faster than light flight! H. David Froning, a 30-year veteran engineer who worked on several designs for future space travel propulsion, gives us this exceptional compilation of his discoveries, struggles and experiences in the realm of faster than light space travel. Central to the concept of faster than light travel is that the vacuum of space itself (the spacetime metric) can be utilized in propulsion systems. “Engineering the vacuum,” as this is called, involves discovering how space can be altered to provide energy/thrust for future spacecraft. Packed with diagrams, some of which show how, as a starship accelerates away from Earth, it disappears and reappears in only seconds. But during these seconds of disappearance, the ship, in effect, leaps high above space-time and over stupendous distances to reach speeds that are billions of times greater than light-speed. Lots of great material on quantum vacuum power, anti-gravity propulsion effects, the velocity of light in spacetime altered regions, effective mass in spacetime-altered regions, warp drives, and tons more!

Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory.

This text, directed to the microwave engineers and Master and PhD students, is on the use of electromagnetics to the development and design of advanced integrated components distinguished by their extended field of applications. The results of hundreds of authors scattered in numerous journals and conference proceedings are carefully reviewed and classed. Several chapters are to refresh the knowledge of readers in advanced electromagnetics. New techniques are represented by compact electromagnetic–quantum equations which can be used in modeling of microwave-quantum integrated circuits of future In addition, a topological method to the boundary value problem analysis is considered with the results and examples. One extended chapter is for the development and design of integrated components for extended bandwidth applications, and the technology and electromagnetic issues of silicon integrated transmission lines, transitions, filters, power dividers, directional couplers, etc are considered. Novel prospective interconnects based on different physical effects are reviewed as well. The ideas of topology is applicable to the electromagnetic signaling and computing, when the vector field maps can carry discrete information, and this area and the results in topological signaling obtained by different authors are analyzed, including the recently designed predicate logic processor operating spatially represented signal units. The book is rich of practical examples, illustrations, and references and useful for the specialists working at the edge of contemporary technology and electromagnetics.

Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in this book examines the consequences of adopting the modified model in the description of atomic structures. The possibility of handling 'photons' in a deterministic way indeed gives a chance to review the foundations of quantum physics. Atoms and molecules are described as aggregations of nuclei and electrons joined through organized photon layers resonating at various frequencies, explaining how matter can absorb or emit light quanta. Some established viewpoints are subverted, offering an alternative scenario. The analysis seeks to provide an answer to many technical problems in physical chemistry and, at the same time, to raise epistemological questions.

This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. The connection between topology and electromagnetism has been known since the 19th century, but there has been little exposition of its relevance to computational methods in modern topological language. This book is an effort to close that gap. It will be of interest to people working in finite element methods for electromagnetic computation and those who have an interest in numerical and industrial applications of algebraic topology.

The connection between the electric and magnetic fields is fundamental to our understanding of light as electromagnetic waves. The magnetic vector potential lies at the heart of this relation. The idea emerged in the early days of research in electromagnetism but was dismissed for more than half a century until the formulation of quantum electrodynamics. The magnetic vector potential is a pivotal concept with ties to many aspects of physics and mathematics. This book unravels the nature of the magnetic vector potential, highlights its connection to quantum mechanics and superconductivity, and explores the analogy with hydrodynamics.