On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry
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, Hermiti...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/795730 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 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. |
|---|---|
| ISSN: | 1687-9120 1687-9139 |