Symmetries and beam reduction in the matrix formulation of the dynamical theory of fast electrons

A survey of the symmetries of the two-dimensional scattering Hamiltonian of fast electrons is presented in order to minimize the size of the effective diffraction matrix. The principle of the method is to decompose the initial Hilbert space into the irreducible invariant subspaces corresponding to the different irreducible representations of the symmetry group of the Hamiltonian and to perform the diagonalization only into those subspaces which share common representations with the initial state. Both unitary and anti-unitary operators are considered. The analysis is based on space-group representations and applies for both symmorphic and non-symmorphic space groups.