Topological Foundations Of Electromagnetism

The book aims to extend Maxwell theory to non-Abelian group forms, demonstrate the topological foundations of electromagnetism, showcase the multi-disciplinary nature of communications, demonstrate the effectiveness of modulated signals in penetrating media, and demonstrate that geometric (Clifford) algebra is the appropriate algebra for describing modulated signals.

Format: Hardback
Length: 376 pages
Publication date: 22 June 2022
Publisher: World Scientific Publishing Co Pte Ltd

The book aims to achieve several significant objectives. Firstly, it seeks to extend the Maxwell theory, a fundamental framework in electromagnetism, to non-Abelian group forms. This expansion opens up new possibilities for understanding and analyzing complex electromagnetic phenomena in a broader range of systems.

Secondly, the book demonstrates that the foundations of electromagnetism are rooted in topology, a branch of mathematics concerned with the properties of spaces that remain unchanged under continuous deformation. This revelation provides a deeper understanding of the underlying principles governing electromagnetic interactions and their behavior in different environments.

Thirdly, the book highlights the multidisciplinary nature of communications, emphasizing the interplay between physics, mathematics, and engineering in the field. It showcases how communication systems can be designed and optimized using a combination of theoretical principles and practical considerations.

Fourthly, the book demonstrates the effectiveness of modulated signals in penetrating media, such as wires, air, and space. It explores the principles of signal modulation, encoding, and transmission, and how these techniques can be used to enhance communication quality, increase data rates, and mitigate interference.

Fifthly, the book establishes that geometric (Clifford) algebra is the appropriate algebra for describing modulated signals. It explains how geometric algebra provides a concise and efficient framework for representing and manipulating signals with complex symmetry properties, enabling the analysis and design of advanced communication systems.

In summary, the book's aims are to expand the scope of Maxwell theory, demonstrate the topological foundations of electromagnetism, highlight the multidisciplinary nature of communications, showcase the effectiveness of modulated signals, and establish geometric algebra as the appropriate algebra for describing modulated signals. These objectives make the book a valuable resource for researchers, engineers, and students in the fields of electromagnetism, communications, and mathematics.

ISBN-13: 9789811253294
Edition number: Second Edition