Bosonization
In theoretical condensed matter physics and particle physics, bosonization is a mathematical procedure by which a system of interacting fermions in dimensions can be transformed to a system of massless, non-interacting bosons.
The method of bosonization was conceived independently by particle physicists Sidney Coleman and Stanley Mandelstam; and condensed matter physicists Daniel C. Mattis and Alan Luther in 1975. In particle physics, however, the boson is interacting, cf, the Sine-Gordon model, and notably through topological interactions, cf. Wess–Zumino–Witten model.
The basic physical idea behind bosonization is that particle-hole excitations are bosonic in character. However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems. Bosonization is an effective field theory that focuses on low-energy excitations. This is done for Luttinger liquid theory.
Two complex fermions are written as functions of a boson
while the inverse map is given by
All equations are normal-ordered. The changed statistics arises from anomalous dimensions of the fields.
