Modified Group Projector Technique (MGPT) - Computer Implementations of Symmetry

The Wigner's group projector technique, a fundamental tool for application of symmetry in physics, involves the summation over group elements. Therefore it referes to finite (and compact) groups. MGPT uses the formalism of the quantum distant correlations to deal with the general case (e.g. infinite discrete groups in solid state physics and Lie groups in particle physics, infinite dimensional induced representations). Interrelated with differential geometrical objects, MGPT can be applied to gauge groups. Dealing with generators and pulled down induced representations only, MGPT is especially powerful in computer implementations: physical properties of the systems with various symmetries are efficiently studied.

• POLSym^® (POLymer Symmetry) the line groups symmetry is applied in numerical calculations of physical properties of polymers and nanotubes.
• DIPSym (DIPeriodic Symmetry) program handling the systems with diperiodic symmetry (at the moment the irreducible representations are available).
• TBASym (Tight-Binding-Approximation Symmetry) new program for tight-binding electron and phonon bands of 1-2-3D crystals. Completed for monoperiodic crystals, and extended for DOS and optical absorption calculations.