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The Principle of Least Action
History and Physics

$140.00 (C)

  • Date Published: April 2018
  • availability: Available
  • format: Hardback
  • isbn: 9780521869027

$ 140.00 (C)

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About the Authors
  • The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.

    • Drawing from the original sources, this book discusses many of the key ideas in this area from both the scientific and historical perspectives to paint a broad picture of this unifying principle
    • Discusses classic papers in a way that is accessible to the modern reader and will appeal to those who are interested in how physical concepts are generated
    • Includes worked examples to show how the principle works in practice
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    Reviews & endorsements

    'I recommend this exciting book to readers interested in how a small number of principles can explain modern physical theory. A major part of this excellent physical, mathematical, and historical study of the principle of least action is the exposition of the optical-mechanical analogy that led to the invention of Schrӧdinger’s wave mechanics in 1926 … Containing the mathematical steps of numerous detailed derivations with clearly designed figures to aid the reader, the text is physically and mathematically rigorous and serves as a guide to the next step: the reading of the original papers cited in the references.' Barry R. Masters, Optics & Photonics News

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    Product details

    • Date Published: April 2018
    • format: Hardback
    • isbn: 9780521869027
    • length: 266 pages
    • dimensions: 254 x 179 x 16 mm
    • weight: 0.67kg
    • contains: 96 b/w illus. 1 table
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Prehistory of variational principles
    3. An excursio to Newton's Principia
    4. The optical-mechanical analogy, part I
    5. D'Alembert, Lagrange, and the statics-dynamics analogy
    6. The optical mechanical analogy, part II: the Hamilton–Jacobi equation
    7. Relativity and least action
    8. The road to quantum mechanics
    Appendix A. Newton's solid of least resistance using calculus
    Appendix B. Original statement of D'Alembert's principle
    Appendix C. Equations of motion of MacCullagh's ether
    Appendix D. Characteristic function for a parabolic Keplerian orbit
    Appendix E. Saddle paths for reections on a mirror
    Appendix F. Kinetic caustics from quantum motion in one dimension
    Appendix G. Einstein's proof of the covariance of Maxwell's equations
    Appendix H. Relativistic four vector potential
    Appendix I. Ehrenfest's proof of the adiabatic theorem

  • Authors

    Alberto Rojo, Oakland University, Michigan
    Alberto Rojo is Associate Professor at Oakland University, Michigan. He is a Fulbright specialist in Physics Education and was awarded the Jack Williams Endowed Chair in Science and Humanities from the University of Eastern New Mexico. His research focuses primarily on theoretical condensed matter and he has previously published books in the popular science field.

    Anthony Bloch, University of Michigan, Ann Arbor
    Anthony Bloch is the Alexander Ziwet Collegiate Professor of Mathematics at the University of Michigan, Ann Arbor. He has received various awards including a Presidential Young Investigator Award, a Guggenheim Fellowship, a Simons Fellowship, and he is Fellow of the Institute of Electrical and Electronics Engineers (IEEE), the Society for Industrial and Applied Mathematics (SIAM), and the American Mathematical Society (AMS). He has served on the editorial boards of various journals and is currently Editor-in-Chief of the SIAM Journal of Control and Optimization.

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