严格孤立非零质量粒子的健全相对论性量子力学及其量子场混响
Sound relativistic quantum mechanics for a strictly solitary nonzero-mass particle, and its quantum-field reverberations
摘要：
一般认为，Klein-Gordon方程和Dirac哈密顿量由于负能量解的不利影响，不能产生可靠的孤立子相对论量子力学;相反，他们的场量子化波函数被重新解释为同时处理粒子和反粒子--尽管反粒子与粒子之间有着明显的物理可分离性，而且根据经验，CP不变性也有轻微的破坏。自由相对论性孤立粒子的自然平方根哈密顿量被迭代以获得克莱因-戈登方程，并被线性化以获得狄拉克哈密顿量，这些步骤具有计算而非物理动机，并且产生上述有问题的负能量解作为无关的伪影。由于自由相对论孤立粒子的自然平方根哈密顿量相反地产生物理上无可挑剔的量子力学，本文着重于扩展该哈密顿量来描述孤立粒子（自旋为0或自旋为1/2）与外部电磁场的相对论相互作用。这是通过使用洛伦兹协变的孤立粒子四动量技术以及假设众所周知的非相对论动力学适用于粒子的静止框架来实现的。洛伦兹不变的孤立粒子的行动，其形式的哈密顿是一个等价的替代方法，以及明确显示。有人提出，两个独立的孤立粒子波函数，一个用于粒子，另一个用于其反粒子，被独立量子化，以代替“重新解释”负能量解-这实际上甚至不会影响真正的孤立粒子。
英文摘要：
It is generally acknowledged that neither the Klein-Gordon equation nor the Dirac Hamiltonian can produce sound solitary-particle relativistic quantum mechanics due to the ill effects of their negative-energy solutions; instead their field-quantized wavefunctions are reinterpreted as dealing with particle and antiparticle simultaneously--despite the clear physical distinguishability of antiparticle from particle and the empirically known slight breaking of the underlying CP invariance. The natural square-root Hamiltonian of the free relativistic solitary particle is iterated to obtain the Klein-Gordon equation and linearized to obtain the Dirac Hamiltonian, steps that have calculational but not physical motivation, and which generate the above-mentioned problematic negative-energy solutions as extraneous artifacts. Since the natural square root Hamiltonian for the free relativistic solitary particle contrariwise produces physically unexceptionable quantum mechanics, this article focuses on extending that Hamiltonian to describe a solitary particle (of either spin 0 or spin one-half) in relativistic interaction with an external electromagnetic field. That is achieved by use of Lorentz-covariant solitary-particle four momentum techniques together with the assumption that well-known nonrelativistic dynamics applies in the particle's rest frame. Lorentz-invariant solitary particle actions, whose formal Hamiltonization is an equivalent alternative approach, are as well explicitly displayed. It is proposed that two separate solitary-particle wavefunctions, one for a particle and the other for its antiparticle, be independently quantized in lieu of "reinterpreting" negative energy solutions--which indeed don't even afflict proper solitary particles.
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