Finsleroid-相对论时间-非对称空间与量子化场
Finsleroid--Relativistic Time--Asymmetric Space and Quantized Fields
摘要：
对于定义良好的芬斯勒相对论性空间$\cE_g^{SR}$（上面的SR表示特殊相对论性），由于只考虑了一个特征参数$g$，它测量了几何与其伪欧几里德前身的偏差，创建相应的相对论性物理场的量子化程序似乎是一项紧迫的任务。该参数可以在所有实数范围上取值;在$g=0$，空间被缩减为普通的伪欧几里德空间。在目前的工作中，制定理论的相对论性物理场在这样的空间开始。基于共形平坦性，提出了求解标量场、电磁场和旋量场方程的一般方法。在任意的参数值下，相对论场相对于出现的非平面波的展开被发现，这提供了一个可以在Finsleroid相对论方法的上下文中量子化场的基础。值得注意的是，监管机构可以自然地提出，以克服相对论性场积分的分歧。提出了各自的关键和基本概念。简而言之，缩写FMF，FMT和FHF将分别用于芬斯勒相对论性度量函数，相关的度量张量和相关的哈密顿函数。
英文摘要：
For well-defined Finsleroid-relativistic space $\cE_g^{SR}$ (with the upperscript SR meaning Special-Relativistic) due only to accounting a characteristic parameter $g$ which measures the deviation of the geometry from its pseudoeuclidean precursor, the creation of the respective quantization programs for relativistic physical fields seems to be an urgent task. The parameter may take on the values over all the real range; at $g=0$ the space is reduced to become an ordinary pseudoeuclidean one. In the present work, the formulation of theory for relativistic physical fields in such a space is initiated. A general method to solve respective scalar, electromagnetic, and spinor field equations is proposed basing on the conformal flatness. At any value of the parameter, the expansion of the relativistic fields with respect to non-plane waves appeared is found, which proposes a base upon which the fields can be quantized in context of the Finsleroid-relativistic approach. Remarkably, the regulators can naturally be proposed to overcome divergences in relativistic field integrals. The respective key and basic concepts involved are presented. For short, the abbreviations FMF, FMT, and FHF will be used for the Finsleroid-relativistic metric function, the associated metric tensor, and the associated Hamiltonian function, respectively.
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