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

Abstract EN

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 SU(n) is equivalent to the product of a single matrix of On2-1 by a real vector.

We recall how Pauli matrices are the adequate tool when n=2 and show how the same is achieved for n=3 with Gell-Mann matrices.