Bosonization

introduction

Bosonization is a nonperturbative method. The Tomonaga-Luttinger (TL) model, a continuum theory of interacting fermions, can be translated into a theory of noninteracting bosons and solved exactly
Bosonization is a method for translating a fermionic theory into a bosonic theory, and eventually retranslating part of the latter into a new fermionic language (cf. the Luther-Emery model or the use of Majorana fermions). This translation process is exact in the continuum limit, but does not warrant an exact solution of the model, except in a few exceptional cases (e.g. the TL model). For the rest, one must rely on renormalization-group analyses, which generally complement bosonization.

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http://www.thphys.uni-heidelberg.de/~komnik/ws1011.html

[1]

Thirring model

Tomonaga-Luttinger model

CFT and bosonization

The intimate relation between CFT and the conventional bosonization had became manifest when Dotsenko and Fateev represented the CFT correlation functions in terms of correlators of bosonic exponents (1984).