History
Grassmann describes an abstract operation called evolution, which he illustrates by applying it in a particular form to generate higher-dimensional geometric objects from lower-dimensional ones [6].
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Application of Geometric Algebra to Electromagnetic Scattering The Clifford-Cauchy-Dirac Technique
Application of Geometric Algebra to Electromagnetic Scattering
Andrew Seagar
Application of Geometric Algebra to Electromagnetic Scattering The Clifford-Cauchy-Dirac Technique
123
Andrew Seagar Gold Coast, QLD Australia
ISBN 978-981-10-0088-1 DOI 10.1007/978-981-10-0089-8
ISBN 978-981-10-0089-8
(eBook)
Library of Congress Control Number: 2015954612 Springer Singapore Heidelberg New York Dordrecht London © Springer Science+Business Media Singapore 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media Singapore Pte Ltd. is part of Springer Science+Business Media (www.springer.com)
To Cathy
Preface
Electromagnetism immediately captured my interest when I was first introduced to it as a student at university. Complete mastery of one of the fundamental phenomena of our physical world seemed within reach, as promised in the form of Maxwell’s equations [1]1. However, the realisation of that promise was not as straightforward as I might have first imagined. Exposure to electromagnetic theory in the period during and immediately following university, with its application to impedance imaging, left me with some skills—largely restricted to two dimensions and quasi-static fields. I found the conventional treatments at that time for fully three-dimensional time-varying fields clumsy and unpalatable. I took that to reflect my own inadequacy in grasping the methods rather than reflecting any inadequacy in the methods themselves. As it turns out, I was mistaken. The first inkling that there might really be a simpler way came for me in 2002 with the paper of Axelsson, Grognard, Hogan and McIntosh [2]. At that time I started to seriously follow the literature relating to the theory of monogenic functions expressed in Clifford’s algebra [3, 4] based on his interpretation of Hamilton’s quaternions [5] in terms of Grassmann’s extens
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