标题： 时空的Finsler型变形非常特殊相对论实现 显示英文标题

标题： The Finsler Type of Space-time Realization of Deformed Very Special Relativity

摘要： 我们在此研究了各种半直积庞加莱子群及其变形伙伴作用下的所有可能的不变度量函数。 该研究穷尽了科恩-格拉肖非常特殊相对论和吉布斯-戈米斯-波普的变形非常特殊相对论方法的可能理论框架。 在芬斯勒-闵可夫斯基类型的时空中，我们发现大多数情况下，无论是原始庞加莱子群还是变形子群，时空都呈现出芬斯勒类型的几何结构。 我们从几何观点解释了即使在破坏洛伦兹对称的理论中也应保持旋转操作的原因。 我们还发现，对于$DTE3b$，TE(2)，ISO(3) 和 ISO(2,1) 的允许几何实际上由一个家族组成，其中度量函数随着特定变量组合的任意函数而变化。 从该家族中选择正确几何的唯一原则只能是时空中物理的动力学行为。 显示英文摘要

摘要： We investigate here all the possible invariant metric functions under the action of various kinds of semi-direct product Poincar\'e subgroups and their deformed partners. The investigation exhausts the possible theoretical frameworks for the spacetime realization of Cohen-Glashow's very special relativity and the deformation very special relativity approach by Gibbons-Gomis-Pope. Within Finsler-Minkowski type of spacetime, we find that the spacetime emerge a Finsler type of geometry in most cases both for undermed Poincar\'e subgroup and for deformed one. We give an explanation that the rotation operation should be kept even in a Lorentz violating theory from geometrical view of point. We also find that the admissible geometry for $DTE3b$, TE(2), ISO(3) and ISO(2,1) actually consists of a family in which the metric function vary with a freedom of arbitrary function of the specified combination of variables. The only principle for choosing the correct geometry from the family can only be the dynamical behavior of physics in the spacetime.