标题： 具有局部相对论对称性的芬斯勒空间 显示英文标题

标题： Finslerian spaces possessing local relativistic symmetry

摘要： 研究表明，高能宇宙射线物理中出现的情况（GZK截断的缺失）所暗示的在洛伦兹因子$\gamma >5\times 10^{10} ,$下可能违反洛伦兹变换的问题，有一个非平凡的解决方案。其本质在于发现了所谓的广义洛伦兹变换，这些变换似乎能够在任意$\gamma .$值下正确连接惯性参考系。与通常的洛伦兹变换一样，广义变换也是线性的，具有群性质，并且导致三维速度的爱因斯坦加法定律。然而，它们的几何意义有所不同：它们是平直各向异性芬斯勒事件空间的相对论对称变换，而不是闵可夫斯基空间的。研究考虑了两种推广局部各向同性的相对论黎曼时空的芬斯勒空间，即部分和完全破坏局部三维各向同性的芬斯勒空间。研究提出了基本相互作用理论相应的推广论据，并针对由于时空局部各向异性而产生的具体物理效应进行了探讨。 显示英文摘要

摘要： It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $\gamma >5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence of the GZK cutoff), has a nontrivial solution. Its essence consists in the discovery of the so-called generalized Lorentz transformations which seem to correctly link the inertial reference frames at any values of $\gamma .$ Like the usual Lorentz transformations, the generalized ones are linear, possess group properties and lead to the Einstein law of addition of 3-velocities. However, their geometric meaning turns out to be different: they serve as relativistic symmetry transformations of a flat anisotropic Finslerian event space rather than of Minkowski space. Consideration is given to two types of Finsler spaces which generalize locally isotropic Riemannian space-time of relativity theory, e. g. Finsler spaces with a partially and entirely broken local 3D isotropy. The investigation advances arguments for the corresponding generalization of the theory of fundamental interactions and for a specific search for physical effects due to local anisotropy of space-time.