Tensor Representations

Abstract

Tensor representations, synonymous for product representations and their decomposition into irreducible constituents, are useful concepts for the treatment of several problems in spectroscopy. Important examples are the classification of the electronic states in atoms and the derivation of selection rules for infrared absorption or the vibrational Raman or hyper-Raman effect in crystals. This article presents first the basics of group theory (group postulates, conjugate elements and classes, representations of groups…) and the formalism of 3 nj symbols. The property tensors are then discussed.