从正则不变性导出相对论性“真时”量子演化方程
Derivation of the relativistic "proper-time" quantum evolution equations from Canonical Invariance
摘要：
根据1）能量算符的谱分辨率; 2）物理观测量与量子厄米算符对应的线性性; 3）经典力学中共轭坐标动量变量的定义; 4）相空间中物理点在一对共轭变量到另一对共轭变量的（正则）变换下保持不变的事实，我们能够证明|E_s>表示为a*exp[-iE_s t_s/ \hbar ]，由此得到了本征时的静能演化方程i \hbar{\partial/\partial t_s}| Psi>= \hat{E_s}| Psi>.对于特殊的相对论情况，这个方程可以简化为通常的i \hbar{\partial/\partial t}| Psi>= \hat{E}| Psi>动力学方程，其中t是“参考时间”，E是总能量。扩展这些方程的加速帧，然后提供。
英文摘要：
Based on 1) the spectral resolution of the energy operator; 2) the linearity of correspondence between physical observables and quantum Hermitian operators; 3) the definition of conjugate coordinate-momentum variables in classical mechanics; and 4) the fact that the physical point in phase space remains unchanged under (canonical) transformations between one pair of conjugate variables to another, we are able to show that <t_s|E_s>, the proper-time rest-energy transformation matrices, are given as a*exp[-iE_s t_s/\hbar], from which we obtain the proper-time rest -energy evolution equation i\hbar{\partial/\partial t_s} |Psi>= \hat{E_s}|Psi>. For special relativistic situations this equation can be reduced to the usual i\hbar{\partial/\partial t}|Psi>=\hat{E}|Psi> dynamical equations, where t is the "reference time" and E is the total energy. Extension of these equations to accelerating frames is then provided.
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