Zusammenfassung
This document outlines the usage of a series of python 2.7 scripts designed
to easily and efficiently create compound operators. This is accomplished by
computing tensor products of smaller building blocks that transform irreducibly
under lattice cubic rotational and translational symmetry. In particular, the
code has the ability to handle representations of the cubic rotation group with
any spatial momentum. The key paradigm is to track the momentum separately from
the rotations, fully utilizing the abelian structure of the translation
subgroup. This goes through the Wigner little group method to classify the
subgroup of rotations that leave the momentum direction unchanged. Using little
groups circumvents the issue of a volume factor in the number of representation
matrices that are needed, instead only requiring the 96 cubic rotation
representation matrices. Tensor products are computed with character tables and
Clebsch-Gordan coefficients are saved for each decomposition in the tensor
product. The code also builds operators in a consistent basis, ensuring that
operators that transform in the same representation have the same properties.
Nutzer