The Bosonization Of One-dimensional Fermi Systems

Along with the developing of application in condensed matter physics,the quantum field theory became a basic solution,which is used to depict the physical phenomena,know of its physics and reason out the principal law. The most successful example is Landau's Fermi liquid model,which is successfully used to interpret the properties of some simple metals. When there's weak interaction the appropriate depiction of the electron in condensed matter is Feimi liquid.Every one of the weak coupling electrons seems being circled by all the electons but itself, which result in the collective excitation called quasi-particle,and the state of quasi-particles is similar to that of free electron gas.This depiction has been already applied to many kinds of condensed matter. It's come to full development on two or three dimensional systems.But it's not a much appropriate model on one-dimensional systems because of infrared divergences when many-body pertebation theory is used,thus this normal solution failed.Therefore we need a new model.the non-Fermi liquid model appears.In fact,there are still much many materials with characteristics of non-Fermi liquid.Especially in mesoscopic systems,Luttinger model is usually used to described the mesoscopic persistent current., this model is a non-Fermi liquid model. To solve this model, the bosonization is introduced by Kane and Fisher.The validity of bosonization be established in quantum field theory here.We discuss briefly the quantum field theory in condensed matter in this paper.Although ,field theories should not be pushed too close to their natural cutoff and a quantitative determination of all the parameters of the theory is not possible in this case, yet some universal(i.e.,unaffected by the details of the microscopic theory)predictions are possible,and are the main target of fields theory of condensed matter systems.The basic idea behind bosonization is that particle-hole excitations are bosonic in character,and that somewhat the greatest part (if not the totality)of the electron gas spectrum might be exhausted by these excitations.The question was raised by F.Bloch...