Algebraic methods in spectroscopy

At present, two main types of algebraic methods are employed for analysis of molecular spectra. The first goes back to the early days of molecular spectroscopy. The second, developed recently by Iachello and coworkers, grew out of nuclear physics and makes use of classical Lie algebras such as SU(4). In this review, the standard spectroscopic fitting Hamiltonian for molecular vibrations, including resonance interactions, is first described. Then, new developments in the application of the standard approach are surveyed. In particular, the question of how one determines the true nature of molecular motions in highly excited spectra is investigated. Next, the recent algebraic approach of Iachello and coworkers is discussed. Application of ideas of molecule-like modes and algebraic methods to the analysis of the electronic spectra of atoms is discussed. Finally, prospects for future development of algebraic methods are discussed.