Variational Principles in Physics

ISBN-13: 9783031216916 / Angielski / Twarda / 2023 / 232 str.

Jean-Louis Basdevant

Opis

Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be a cornerstone of geometrical optics. This book explains variational principles and charts their use throughout modern physics. It examines the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. The book also offers simple but rich first impressions of Einstein’s General Relativity, Feynman’s Quantum Mechanics, and more that reveal amazing interconnections between various fields of physics.

Spis treści

Chapter 1. Structure of physical theories.- Chapter 2. Variational Principles.- Chapter 3. The Analytical Mechanics of Lagrange.- Chapter 4. Hamilton’s canonical formalism.- Chapter 5. Action, Optics, Hamilton-Jacobi equation.- Chapter 6. Lagrangian Field Theory.- Chapter 7. Motion in a Curved Space.- Chapter 8. Gravitational waves.- Chapter 9. Feynman’s Path Integrals in quantum Mechanics

O autorze

Jean-Louis Basdevant, graduated from Ecole Normale Supérieure (1958-1963), Ph.D. at Strasbourg University (1967), is Assistant Researcher and Director of Research at the CNRS (1963-2007), CERN (1970-1972), Professor at the Ecole Polytechnique (1969-2004), and Nominated Honorary Professor (2004).

Blurb

This revised and enhanced new edition of a well-established textbook provides a balanced overview of various areas of theoretical physics based on the use of variational principles. As well as field theory, the book deals with motion in curved spaces, the cradle of general relativity, and gravitational optics. New chapters on the relation of classical mechanics and geometrical optics as well as gravitational waves, which are considered as a true confirmation of general relativity, have been included. Each chapter has been carefully revised and enlarged. Finally, the text describes Feynman's formulation of quantum mechanics by path integrals, which gives the link between quantum and classical mechanics.

The book provides a set of exercises, problems, and solutions.