The Principle of Least Action: History and Physics
Cambridge University Press, 3/29/2018
EAN 9780521869027, ISBN10: 0521869021
Hardcover, 266 pages, 25.4 x 17.9 x 1.6 cm
Language: English
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.
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.