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© 2004

Mathematical Theory of Diffraction

  • Authors

Benefits

  • The extensive notes by the translators are rich in historical background

  • Provides many technical details for the reader

Book

Part of the Progress in Mathematical Physics book series (PMP, volume 35)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Arnold Sommerfeld
    Pages 1-8
  3. A. Sommerfeld
    Pages 9-68
  4. Back Matter
    Pages 69-157

About this book

Introduction

Arnold Sommerfeld's Mathematical Theory of Diffraction marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics.

This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader. A detailed account of the previous diffraction analyses of Kirchhoff and Poincaré provides a context for the striking originality and power of Sommerfeld's ideas.

The availability of this translation is an enriching contribution to the community of mathematical and theoretical physicists.

Keywords

History of Mathematics diffraction mathematical physics optical theory wave equation

Bibliographic information

Reviews

From the reviews:

“This is a very nice book for those interested in the theory of diffraction since it presents, for the first time in English, the strikingly original work of Sommerfeld—which marks a milestone in optical theory—enriched with historical background and technical details. The interest of this book is not only historical but also technical as it presents a surprisingly rich and complex mix of pure and applied mathematics.”(MATHEMATICAL REVIEWS)

"This book offers the first publication in English of Sommerfeld’s original work, together with extensive notes by the translators, and it can be recommended to anyone interested in the theory of diffraction. … The translator’s notes (64 pages) are very illuminating for the reader by providing a lot of historical remarks, technical details, and a nice account of previous diffraction analyses of Kirchhoff and Poincaré." (Johannes Elschner, Zentralblatt MATH, Vol. 1109 (11), 2007)