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Advances in Mathematical Physics
Volume 2014, Article ID 795730, 14 pages
http://dx.doi.org/10.1155/2014/795730
Research Article

On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry

CTMM, Institut Charles Gerhardt Montpellier, CNRS/Université Montpellier 2, CC 15001, Place Eugène Bataillon, 34095 Montpellier, France

Received 25 March 2014; Accepted 22 May 2014; Published 15 July 2014

Academic Editor: Fabien Gatti

Copyright © 2014 Benjamin Lasorne. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A formulation based on Lie group homomorphisms is presented for simplifying the treatment of unitary similarity transformations of Hamiltonian matrices in nonadiabatic photochemistry. A general derivation is provided whereby it is shown that a similarity transformation acting on a traceless, Hermitian matrix through a unitary matrix of is equivalent to the product of a single matrix of by a real vector. We recall how Pauli matrices are the adequate tool when and show how the same is achieved for with Gell-Mann matrices.