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

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  • Benjamin Lasorne

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.

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  • Benjamin Lasorne, 2014. "On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-14, July.
    • Handle: RePEc:hin:jnlamp:795730
    DOI: 10.1155/2014/795730
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