Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.