The Principle of Least Action

Erscheinungsjahr 2018
ISBN: 978-0-521-86902-7
Verlag: Cambridge University Press

Buch, Englisch, 278 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 647 g

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.

Autoren/Hrsg.

Rojo, Alberto

Bloch, Anthony

Fachgebiete

• Naturwissenschaften Physik Mechanik
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

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; References; Index.

Über Autor(innen)

Bloch, Anthony
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.

Rojo, Alberto
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.