臺灣博碩士論文加值系統

馬克士威方程組基本上是由電學和磁學的實驗結果代入理論考量從而得到的，其中一些方程式可以從更基本的物理條件，如牛頓第二運動定律以及位置與速度的對易關係或非量子化情況下由帕松運算所推導以得出。
在這篇論文中，我們首先介紹Dyson以量子力學的形式對於Feynman's proof所進行的推導，並得到其中兩個馬克士威方程式以及勞倫茲力。接著介紹Hughes利用古典力學推導出的非相對論性粒子的相同方程組以及Montesinos和Pérez-Lorenzana 所推導出的相對論性粒子的情形。由於馬克士威方程組和勞倫茲力定律本來就是以古典的形式寫成，其推導自然可奠基於古典物理下。
最後，由於馬克士威方程組整體為了符合狹義相對論而遵守勞倫茲轉換，其推導也須遵守勞倫茲轉換之形式。

Maxwell equations were basically constructed from the results of experiments of electricity and magnetism with theoretical considerations. It was shown that some of the equations can be derived from some basic conditions, such as Newton's second law and the commutation relations or Poisson brackets between positions and velocities.
In this thesis, two of the Maxwell equations and the Lorentz force law are derived from Feynman's proof based on the formalism of quantum mechanics as described by Dyson. The equations are also obtained by using the rules of classical mechanics for a non-relativistic particle as shown by Hughes, and for a relativistic particle by Montesinos and Pérez-Lorenzana. It is shown that since the Maxwell equations and the Lorentz force law are classical equations, their derivations can be based on the rules of classical physics. Also, since the set of four Maxwell equations is Lorentz invariant, the derivation of the Maxwell equations has to be based on a Lorentz invariant formalism, obeying the principles of special relativity.

1 Introduction 1
2 Review of the Maxwell Equations 3
3 Feynman’s Proof of the Maxwell Equations 7
4 Poisson Brackets 13
4.1 Classical Non-Relativistic Particle . . . . . . . . . . . . . . . . . . . . . 13
4.2 Classical Relativistic Particle . . . . . . . . . . . . . . . . . . . . . . . 19
5 Summary 25
A The Jacobi Identity 27
B The Electromagnetic Fields 29
Bibliography 31

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