中文摘要：

当今物理实验对局域Lorentz和CPT对称性的破缺程度给出了严格的限制,但同时有诸多细微现象都似乎表示这两者可能是破缺的.找到这种可能的破缺并给出匹配的合理的物理图景,将是一件很有意义的事情.由于对所有洛伦兹子群与时空平移群的半直积群进行形变所可能得到的形变群其相应的时空几何实现基本都是Finsler类型的,在本文中研究了这些时空几何中的质点动力学,得到了其色散关系,并据此研究了这些Finsler时空所容许的场论模型,讨论了标量场、旋量场、矢量场和规范耦合的动力学和相对闵氏时空中场论由形变引起的修正.本文选择研究的Finsler结构,具有明显的时空方向依赖性的.因而,如果时空是Finsler的,那么可以通过某些精心设计的实验观测到这种方向依赖性.

英文摘要：

The modern experiments have put strict restrictions on the possible violation of local Lorentz and CPT invariance. However there seem to exist some clues showing that the two symmetries are possibly broken. It would be remarkable to find out the possible breaking mechanism and build up a reasonable framework with Lorentz or CPT violation. As the spacetime corresponding to all possible of deformation of all the Poincaré subgroups of the forms of semi product of the Lorentz subgroup with the spacetime translation are almost of Finsler type. We study here the particle dynamics in these Finsler spacetime and investigate their dispersion relations based on which we investigate the possible self-consistent field theories dynamics in the Finsler spacetime including scalar field,spinor field,vector field and gauge coupling. The modifications caused by deformation relative to field theories in Minkowski spacetime are discussed. The Finsler structures we study in this paper have strong dependence on the space-time direction. Thus,if space-time is of Finsler type,we can observe the dependence by well designed experiment.