Strong-coupling limit for a mobile particle in a fermionic bath

The behavior of a single particle interacting with a Fermi liquid is dominated by two competing effects: due to a large number of low energy excitations of the Fermi sea (orthogonality catastrophe), the fermions cannot follow the particle adiabatically leading to a destruction of coherence. On the other side the recoil energy reduces the available phase space for scattering events thereby favoring coherent behavior. We implement these two aspects exactly by an effective action. In dimensions d > 1 this leads to a finite quasiparticle weight, while in d = 1 the Green's function decays algebraically. Here we discuss the case of very strong coupling: A new low-energy scale shows up, controlling the qualitative behavior of the diverging incoherent part of the spectral function.