张量不变式方法在物理张量计算中的应用——(Ⅰ)原理

Application of Method of Tensor Invariants to the Calculation of Physical Tensors of Crystals——(I) Principles

对张量不变式方法进行了改造和推广,系统地阐明了它的基本原理和使用步骤。提出了伴随基定理和独立基个数定理,并在此基础上得到了所有晶体点群的一到三秩同变正交基,使得张量不变式方法能够简便、准确地用于所有常用的物理张量的计算。

The method of tensor invariants (MTI) to determine the components of physical tensors is improved and generalized.The principles of MTI and the procedure of its application are elaborated systematically.Based upon the theorems of shadow and the number of independent tesor components,all the isovariant orthogonal bases up to rank 3 for 32 crystal point groups are listed,so the method is easily applied to all cases of physical tensors that in common use.