We generalize the momentum average approximation to study the properties of single polarons in models with boson affected hopping, where the fermion-boson scattering depends explicitly on both the fermions and the bosons momentum. As a specific example, we investigate the Edwards fermion-boson model in both one and two dimensions. In one dimension, this allows us to compare our results with exact diagonalization results, to validate the accuracy of our approximation. The generalization to two-dimensional lattices allows us to calculate the polarons quasiparticle weight and dispersion throughout the Brillouin zone and to demonstrate the importance of Trugman loops in generating a finite effective mass even when the free fermion has an infinite mass.
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