论文标题
狄拉克和路径积分
Dirac and the Path Integral
论文作者
论文摘要
通过对DIRAC 1932年关于拉格朗日量子力学的论文的非常仔细的分析，以及他的经典著作的第二版和第三版，我表明，dirac对Quantum Mechanics的出生的贡献并不限制在Quargrangians上的自然机制，但要在量子机制中示出了量子，但要符合DIRID的方式，但该量子的贡献并不限制在量子机制中，但是我称之为{\ it Dirac Path-integral}的路径综合性，比Feynman的路径综合}具有所有理想的功能。最重要的是，狄拉克路径综合与不可避免的量化歧义完全兼容，而Feynman Path-Integral却永远无法具有那么完整的一致性。我特别表明，费曼的主张是，对于无限的时间间隔，狄拉克认为是类似物实际上是成比例的，永远无法始终是正确的。我还展示了狄拉克路径综合和schrödinger方程之间的分解。特别是，表明每种选择狄拉克路径综合会产生一个{\ it量子hamiltonian}，它与Feynman Path-intergement fress fres fe and cass classical contemental均具有相同的{\ it Classical Analogue}。迪拉克（Dirac）以最直接的方式将经典力学的最小动作原理概括为所有广义路径综合性的方法。
Through a very careful analysis of Dirac's 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {\it The Principles of Quantum Mechanics}, I show that Dirac's contributions to the birth of the path-integral approach to quantum mechanics is not restricted to just his seminal demonstration of how Lagrangians appear naturally in quantum mechanics, but that Dirac should be credited for creating a path-integral which I call {\it Dirac path-integral} which is far more general than Feynman's while possessing all its desirable features. On top of it, the Dirac path-integral is fully compatible with the inevitable quantisation ambiguities, while the Feynman path-integral can never have that full consistency. In particular, I show that the claim by Feynman that for infinitesimal time intervals, what Dirac thought were analogues were actually proportional can not be correct always. I have also shown the conection between Dirac path-integrals and the Schrödinger equation. In particular, it is shown that each choice of Dirac path-integral yields a {\it quantum Hamiltonian} that is generically different from what the Feynman path-integral gives, and that all of them have the same {\it classical analogue}. Dirac's method of demonstrating the least action principle for classical mechanics generalizes in a most straightforward way to all the generalized path-integrals.
