Hamiltonian Flow Equations and the Electron-Phonon-Problem
In this thesis we investigate the electron-phonon-system using the method of Flow Equations for Hamiltonians. In this continuous diagonalisation process the one particle energies and interaction constants are subject to a series of transformations, the ``flow'' of the Hamiltonian. They depend on a flow parameter l varying from zero to infinity. We give a proof that the asymptotic behaviour of the flow of the one-particle energies for large l is given by a constnat over squareroot of l behaviour. The constant may contain terms logarithmic in l and depends on electronic momentum k. This result is used to show that the transformation does lead to a blockdiagonal Hamiltonian decoupling the electron and the phonon subsystems. We obtain the same renormalization of the phonon energies as Wegner and Lenz, who neglected the shift of the electronic one-particle energies. The dependency of the renormalization of the electronic energies on the distance to the fermi surface is calculated. We investigate the transformation of the electronic one-particle operators. In the appendix we present a rigorous proof of the asymptotic behaviour. The l-dependency is changed by including an additional logarithmic factor and this refined asymptotic behaviour is investigated.
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