Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled “The Principle of Least Action in Quantum Mechanics, ' its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space-time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied — and transcended — its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space-time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article “Space-Time Approach to Non-Relativistic Quantum Mechanics” [Reviews of Modern Physics 20 (1948), 367-387], Paul Dirac's seminal paper “The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.
Author(s): Laurie M. Brown; Richard P. Feynman
Publisher: World Scientific Publishing Company
Year: 2005
Language: English
Pages: 119
Cover
Half Title
Title
Copyright
Contents
Preface
The Principle of Least Actioin in Quantum Mechanics - Richard P. Feynman
I. Introduction
II. Least Action in Classical Mechanics
1. The Concept of a Functional
2. The Principle of Least Action
3. Conservation of Energy. Constants of Motion
4. Particles Interacting through an Intermediate Oscillator
III. Least Action in Quantum Mechanics
1. The Lagrangian in Quantum Mechanics
2. The Calculation of Matrix Elements in the Language of a Lagrangian
3. The Equations of Motion in Lagrangian Form
4. Translation to the Ordinary Notation of Quantum Mechanics
5. The Generalization to any Action Function
6. Conservation of Energy. Constants of the Motion
7. The Role of the Wave Function
8. Transfer Probabilities
9. Expectation Values for Observables
10. Application to the Forced Harmonic Oscillator
11. Particles Interacting through an Intermediate Oscillator
12. Conclusion
Space-Time Approach to Non-Relativistic Quantum Mechanics - R. P. Feynman
1. Introduction
2. The Superposition of Probability Amplitudes
3. The Probability Amplitude for a Space-Time Path
4. The Calculation of the Probability Amplitude for a Path
5. Definition of the Wave Function
6. The Wave Equation
7. Discussion of the Wave Equation: The Classical Limit
8. Operator Algebra: Matrix Elements
9. Newton's Equations: The Commutation Relation
10. The Hamiltonian: Momentum
11. Inadequacies of the Formulation
12. A Possible Generalization
13. Applications to Eliminate Field Oscillators
14. Statistical Mechanics: Spin and Relativity
The Lagrangian in Quantum Mechanics - P. A. M. Dirac
Contact Transformations
The Lagrangian and the Action Principle
Application to Field Dynamics
