  Employing a self-consistent (optimized) variational diagonalization scheme,
we investigate the formation of polaronic quasiparticles in a spinless
fermion-boson transport model that couples the movement of charge carriers to
fluctuations and correlations of a background medium. The background is
parameterized by bosonic degrees of freedom. The variational fermion-boson
Hilbert space is constructed to achieve high accuracy in one to three spatial
dimensions with modest computational requirements. To characterize the
ground-state properties of the Edwards model in the single-particle sector, we
present exact numerical results for the polaron band dispersion, quasiparticle
weight, Drude weight, mass enhancement, and the particle-boson correlations in
a wide parameter regime. In the Edwards model, transport will be quasifree,
diffusive or boson-assisted in the weakly fermion-boson coupled,
fluctuation-dominated or strongly correlated regimes, respectively. Thereby
correlated transport is not only assisted but also limited by the bosonic
excitations. As a result, the Drude weight remains finite even in the limit of
very small boson frequencies. For a strongly correlated background, closed
loops are important, in any dimension, to generate a finite effective particle
mass even when the free fermion has an infinite mass.
