| Abstrakt: |
We have already discussed the arbitrariness of a representation with regard to similarity or equivalence transformations. Namely, if D(Γj)(R) is a representation of a group, so is U−1D(Γj)(R)U. To get around this arbitrariness, we introduce the use of the trace (or character) of a matrix representation which remains invariant under a similarity transformation. In this chapter we define the character of a representation, derive the most important theorems for the character, summarize the conventional notations used to denote symmetry operations and groups, and we discuss the construction of some of the most important character tables for the socalled point groups, that are listed in Appendix A. Point groups have no translation symmetry, in contrast to the space groups, that will be discussed in Chap. 9, and include both point group symmetry operations and translations. [ABSTRACT FROM AUTHOR] |
