Feynman's Thesis: A New Approach to Quantum Theory

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World Scientific, 2005 - Science - 119 pages
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.
 

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Contents

The Principle of Least Action in Quantum Mechanics
1
II Least Action in Classical Mechanics
6
2 The Principle of Least Action
9
3 Conservation of Energy Constants of the Motion
10
4 Particles Interacting through an Intermediate Oscillator
16
III Least Action in Quantum Mechanics
24
1 The Lagrangian in Quantum Mechanics
26
2 The Calculation of Matrix Elements in the Language of a Lagrangian
32
6 Conservation of Energy Constants of the Motion
42
7 The Role of the Wave Function
44
8 Transition Probabilities
46
9 Expectation Values for Observables
49
10 Application to the Forced Harmonic Oscillator
55
11 Particles Interacting through an Intermediate Oscillator
61
12 Conclusion
68
Spacetime Approach to NonRelativistic Quantum Mechanics
71

3 The Equations of Motion in Lagrangian Form
34
4 Translation to the Ordinary Notation of Quantum Mechanics
39
5 The Generalization to any Action Function
41
The Lagrangian in Quantum Mechanics
111
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