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Perhaps one reason that there are comparatively few books on the Dirac equation is the lack of an unambiguous quantum mechanical interpretation. Dirac’s electron theory seems to remain a theory with no clearly defined range of validity, with peculiarities at its limits which are not completely understood. Indeed, it is not clear whether one should interpret the Dirac equation as a quantum mechanical evolution equation, like the Schrodinger equation for single particle. The main difficulty with a quantum mechanical on-particle interpretation is the occurrence of states with negative (kinetic) energy. Interaction may cause transitions to negative energy states, so that there is no hope for a stability of matter within that framework. In view of these difficulties R. Jost stated, “The unquantized Dirac field has therefore no useful physical interpretation”([Jo 65],P.39). Despite this verdict we are going to approach these questions in a pragmatic way. A tentative quantum mechanical interpretation will serve as a guiding principle for the mathemathical development of the theory. It will turn out that the negative energies anticipate the occurrence of antiparticles, but for the simultaneous description of particles and antiparticles one has to extend the formalism of quantum mechanics. Hence the Dirac theory may be considered a step on the way to understanding quantum field theory (see Chapter 10).
或许极少有关于Dirac方程的专门书籍的原因是明确的量子力学性解释的缺乏。Dirac电子理论似乎留给了我们并无明确界定其有效适用范围的一部理论，其特性和应用尺度并不是十分明朗。事实上，人们是否应该将Dirac方程解释为量子力学的进展方程也不是清楚的，像单粒子的Schrodinge方程那样。描写粒子的量子力学性主要困难是负（动能）能量状态的出现。相互作用有可能引起粒子态转化为负能态，因此在其框架内人们不能够指望物质是稳定的。鉴于这一困难，R.Jost表明，“非量子化Dirac场因而无有意义的物理解释”（[Jo 65], P.39）。尽管如此，我们将注重实效地处理这些问题。作为数学理论发展的指导原则，试验性的量子力学描述发挥着重要作用。这导致负能量预示着反物质的重大发现，然而同时对粒子和反粒子的描述人们不得不扩充过去量子力学的形式。因此Dirac理论可以被认为是理解量子场论的一个重要步骤。（参考第10章） |
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发表于 2007-4-30 10:00:02
