On the use of Lie group homomorphisms for treating similarity transformations in nonadiabatic photochemistry (Q471667)

Summary: 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 \(\mathrm{SU}(n)\) is equivalent to the product of a single matrix of \(\mathrm O(N^2-1)\) 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.