GTCharProjectionOperator
GTCharProjectionOperator[classes,characters,function,arguments]
applies the character projection operator corresponding to an irreducible representation to a certain function with given arguments.
Details and Options
- The Projection operator
is given by 
, where 
is the dimension of the irreducible representation 
with characters 
and 
is the order of the group. - The characters
belong to an irreducible representation 
of the group 
. The classes and characters can be obtained using the command GTCharacterTable. - arguments is a list of arguments used by function, typically {x,y,z}
- The following option can be given:
-
GOFast False Controls the input validation GOLattice {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} Gives the lattice vectors in case space groups are considered - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 5.9
Examples
open allclose allBasic Examples (3)
For the example, the point group 
is considered. The point group and the character table are generated as follows:
The function 
will be analysed.
The application of the character projection operator, related to the irreducible representation 
can be calculated by:
and for the irreducible representation 
by:
The same formalism holds for the irreducible representation 
,
GTCharProjectionOperator can also be used for 3-dimensional vector functions.
If a double group is installed, GTCharProjectionOperator can be used for spinor functions.
Generalizations & Extensions (1)
The function 
will be analysed.
If a whole character table is supplied, GTCharProjectionOperator applies the character projection operator for every irreducible representation.
