相对论性量子力学的纤维丛表述。II。协变方法
Fibre bundle formulation of relativistic quantum mechanics. II. Covariant approach
摘要：
提出了相对论量子力学数学基础的纤维丛表述。在现阶段，理论的丛形式与它的常规形式是等价的，但它允许在不同方向上的新类型的推广。在本研究的第二部分，我们考虑相对论性量子力学的丛描述的协变方法。在它的波函数被替换为（状态）部分的适当选择矢量丛在时空的（标准）纤维是空间的波函数。现在量子演化被描述为（总）束空间中态截面的线性输运（通过沿空间\nobreakdash -时间的恒等映射的输运）。发现了相对论性波动方程的（延迟）格林函数与演化算符和输运之间的联系，特别是Dirac方程和Klein-Gordon方程。
英文摘要：
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the present, second, part of our investigation, we consider a covariant approach to bundle description of relativistic quantum mechanics. In it the wavefunctions are replaced with (state) sections of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of the wavefunctions. Now the quantum evolution is described as a linear transportation (by means of the transport along the identity map of the space\nobreakdash-time) of the state sections in the (total) bundle space. Connections between the (retarded) Green functions of the relativistic wave equations and the evolution operators and transports are found. Especially the Dirac and Klein-Gordon equations are considered.
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