Systematic perturbation calculation for a non commutative model for a metallic glas

We present a systematic perturbation calculation up to the 4th order in the interaction for a metallic-glas-model with an anisotropic coupling of the conduction electrons to a local two-level-system. The logarithmic-(infrared-)divergent terms for the electronic lifetime are suppressed by exponentially small prefactors in the region I (ET) whereas in the region II (ET) they survive in the general case of non-commuting elastic and inelastic couplings in the Hamiltonian, whereE denotes the level-splittings of the local-system, the excitation energy of the conduction electrons above the Fermi level, andT the thermal energy.