Single-hole dynamics in the t-J model

The quasiparticle weight of a single hole in an antiferromagnetic background is studied in the semiclassical approximation. We start from the $t\ensuremath{-}J$ model, generalize it to arbitrary spin S by employing an appropriate coherent state representation for the hole, and derive an effective action for the dynamics in the long-wavelength low-energy limit. In the same limit, we find an expression for the single-hole Green's function which we evaluate in an $1/S$ expansion. Our approach has the advantage of being applicable in one and in two dimensions. We find two qualitatively different results in these two cases: while in one dimension our results are compatible with a vanishing quasiparticle weight, this weight is found to be finite in two dimensions, indicating normal quasiparticle behavior of the hole in this last case.