## Feynman's Thesis: A New Approach to Quantum TheoryRichard 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

### Other editions - View all

Feynman's Thesis: A New Approach to Quantum Theory Richard Phillips Feynman No preview available - 1942 |

### Common terms and phrases

action function action principle calculate classical Lagrangian classical mechanics consider constant coordinates corresponding deﬁned deﬁnition depends described diﬀerent diﬀerential diﬃculty discussed eﬀect electromagnetic ﬁeld energy equations of motion equivalent example expected value exponential expression factor Feynman ﬁnal ﬁnd ﬁnite ﬁrst order ﬁxed formulation of quantum Hamiltonian harmonic oscillator inﬁnite integral integrand interaction intermediate oscillator intermediate q’s interval least action limit mathematical matrix element measurement method momentum notation obtained operator P. A. M. Dirac particles path perturbation physical postulate potential principle of least probability amplitude problem qt|qT quantity quantized quantum analogue quantum electrodynamics quantum mechanics quantum theory region relation replaced represent result satisﬁes simple space-time speciﬁed suﬃcient suppose t1 and t2 thesis ti+1 tonian transformation function transition element variables vector potential velocities wave function xi+1 xk+1 zero