绝热变化的芬斯勒流形上的物理学与宇宙学
Physics on the adiabatically changed Finslerian manifold and cosmology
AI总结：
该研究证实普朗克常数是绝热变化芬斯勒流形上电磁场的绝热不变量，提出流形上的电动力学方程，推导量子化、宇宙红移等效应，解释含重子系统的量子化。
摘要：
在本文中，我们证实了此前的研究结果[5]：普朗克常数是在绝热变化的芬斯勒（Finslerian）流形上传播的电磁场的绝热不变量。通过宇宙学参数的直接计算，得到其值为h=6×10^(-27)（尔格·秒）。我们还证实，由于几何结构的变化，普朗克常数（以及其他依赖于h的基本常数）会随时间发生变化。\n 作为示例，我们计算了精细结构常数的变化，其相对变化率((da/dt)/a)为1.0×10^(-18)（1/秒）。\n 我们表明，在以绝热变化几何为特征的芬斯勒流形上，经典自由电磁场会从流形的性质出发被几何化地量子化，使得场的绝热不变量满足ET=6×10^(-27)=h（尔格·秒）。\n 本文提出了芬斯勒流形上的电动力学方程。需要强调的是，量子化自然地从这些方程中产生，且是由流形的绝热变化几何所引发的。我们详细讨论了这些方程的两个直接推论：i）光子的宇宙学红移，以及ii）可直接从所得方程推导得出的阿哈罗诺夫-玻姆（Aharonov–Bohm）效应。研究表明，由电磁场和重子成分（如原子）组成的系统的量子化是显而易见的，且有清晰的解释。
英文摘要：
In present paper we confirm our previous result [5] that the Planck constant is adiabatic invariant of electromagnetic field propagating on the adiabatically changed Finslerian manifold. Direct calculation from cosmological parameters gives value h=6x10(-27) (erg s). We also confirm that Planck constant (and hence other fundamental constants which depend on h) is varied on time due to changing of geometry. As an example the variation of the fine structure constant is calculated. Its relative variation ((da/dt)/a) consist 1.0x10(-18) (1/s). We show that on the Finsler manifold characterized by adiabatically changed geometry, classical free electromagnetic field is quantized geometrically, from the properties of the manifold in such manner that adiabatic invariant of field is ET=6x10(-27)=h(erg s). Equations of electrodynamics on the Finslerian manifold are suggested. It is stressed that quantization naturally appears from these equations and is provoked by adiabatically changed geometry of manifold. We consider in details two direct consequences of the equations: i) cosmological redshift of photons and ii) effects of Aharonov -- Bohm that immediately follow from obtained equations. It is shown that quantization of system consists of electromagnetic field and baryonic components (like atoms) is obvious and has clear explanation.
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