双极化孤立粒子Maxwell无源方程与含时Schroedinger方程的等价性及哈密顿量|cp|
Equivalence of Maxwell's source-free equations to the time-dependent Schroedinger equation for a solitary particle with two polarizations and Hamiltonian |cp|
摘要：
在以前的一篇论文中指出，尽管克莱因-戈登方程和狄拉克哈密顿量都不能产生可靠的孤立自由粒子相对论性量子力学，但非零质量自由粒子的自然平方根相对论性哈密顿量确实能实现这一点。失败的克莱因-戈登和狄拉克理论的审查：孤立狄拉克自由粒子，除其他外，一个不变的速度远远超过c和惊人的自发康普顿加速度，但没有任何病理所产生的平方根相对论性哈密顿量。狄拉克对孤立粒子的与时间相关的组态表象薛定谔方程的四矢量特征的关键误解暴露无遗，狄拉克方程的非相对论极限是泡利方程的标准“证明”也是无效的。洛伦兹从粒子静止坐标系点唯一地提升到平方根哈密顿量，但是对于无质量的粒子，这些不存在。相反，麦克斯韦方程在空间傅立叶变换中被解剖，以分离非动态纵向场自由度和动态横向场自由度。在没有源的情况下解耦后，横向场分量服从两个相同的含时薛定谔方程（由于两个线性极化），该方程具有无质量的自由粒子对角化平方根哈密顿量。这些场很容易被修改以符合孤立子波函数的属性。还导出了辐射规范中波函数与势的关系。然后重复该练习，而没有空间傅立叶变换的相当大的好处。
英文摘要：
It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the Klein-Gordon and Dirac theories are reviewed: the solitary Dirac free particle has, inter alia, an invariant speed well in excess of c and staggering spontaneous Compton acceleration, but no pathologies whatsoever arise from the square-root relativistic Hamiltonian. Dirac's key misapprehension of the underlying four-vector character of the time-dependent, configuration-representation Schroedinger equation for a solitary particle is laid bare, as is the invalidity of the standard "proof" that the nonrelativistic limit of the Dirac equation is the Pauli equation. Lorentz boosts from the particle rest frame point uniquely to the square-root Hamiltonian, but these don't exist for a massless particle. Instead, Maxwell's equations are dissected in spatial Fourier transform to separate nondynamical longitudinal from dynamical transverse field degrees of freedom. Upon their decoupling in the absence of sources, the transverse field components are seen to obey two identical time-dependent Schroedinger equations (owing to two linear polarizations), which have the massless free-particle diagonalized square-root Hamiltonian. Those fields are readily modified to conform to the attributes of solitary-photon wave functions. The wave functions' relations to the potentials in radiation gauge are also worked out. The exercise is then repeated without the considerable benefit of the spatial Fourier transform.
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