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On the other hand, my feeling is that the relativistic quantum mechanics of electrons has a meaningful place among other theories of mathematical physics. Somewhat vaguely we characterize its range of validity as the range of quantum phenomena where velocities are so high that relativistic kinematical effects are measurable, but where the energies are sufficiently small that pair creation occurs with negligible probability. The successful description of the hydrogen atom is a clear indication that this range is not empty. The main advantages of using the Dirac equation in a description of electrons are the following: (1) The Dirac equation is compatible with the theory of relativity (2) it describes the spin of the electron and its magnetic moment in a completely natural way. Therefore, I regard the Dirac equation as one step further towards the description of reality than a one-particle Schrodinger theory. Nevertheless, we have to be aware of the fact that a quantum mechanical interpretation leads to inconsistencies if pushed too far. Therefore I have included treatments of the paradoxes and difficulties indicating the limitations of the theory, in particular the localization problem and the Klein paradox. For these problems there is still no clear solution, even in quantum electrodynamics.
另一方面，我感觉电子的相对论量子力学有其数学物理的意味深长的地方。概略地说，我们刻画了其有效范围是速度如此之高而相对论性运动效应竟可以测量，但物质的能量又是如此之小，典型的例子是其产生的概率极小的正负电子偶。氢原子成功描述清楚表明这一范围并不是空想的。在电子的描述中用Dirac方程描述主要优势有：（1）Diarc方程同相对论理论是一致的；（2）它很自然地描写了电子自旋和自旋磁矩。因此我将Dirac方程作为进一步描述一个粒子以上的Schrodinger方程的一个步骤。然而我们不得不面临着一个残酷的事实，将Dirac方程推向过深入过广泛的范围，那么量子力学就将导致矛盾。因此我们讨论包含了对那些预示着理论局限性的困难和矛盾处理，尤其是局部问题和Klein矛盾。这些问题还没有明确的解释，即使在量子电动力学中。
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发表于 2007-4-29 19:58:14
