Bosonization

introduction

• Bosonization is a nonperturbative method
• 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 Tomonaga-Luttinger model).
• For the rest, one must rely on renormalization-group analyses, which generally complement bosonization.

Tomonaga-Luttinger model

• The Tomonaga-Luttinger (TL) model, a continuum theory of interacting fermions, can be translated into a theory of noninteracting bosons and solved exactly

Thirring model

• Thirring 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)

encyclopedia

• http://en.wikipedia.org/wiki/Bosonization

books

• Bosonization and Strongly Correlated Systems
• http://www.worldscibooks.com/physics/2436.html

expositions

• Bosonization and strongly correlated systems
• A few aspects of bosonization in light front field theory
• http://www.google.com/url?sa=t&source=web&cd=12&ved=0CCIQFjABOAo&url=http%3A%2F%2Fpeople.web.psi.ch%2Fmudry%2FLECTURES_NOTES%2FSPRING10%2Flecture13nup.ps&rct=j&q=bosonization%20massive%20Thirring%20model&ei=lacDTr6WH4jCsAOL7ODoDQ&usg=AFQjCNH-Nz2ksruq-_2OrpT_LlA1do30EA&sig2=FrEt3dJxzpgnD0vj15t3fQ&cad=rja
• E. Miranda, Introduction to bosonization, Braz. J. Phys. vol.33 no.1 São Paulo Mar. 2003
• Rao, Sumathi, and Diptiman Sen. ‘An Introduction to Bosonization and Aome of Its Applications’. arXiv:cond-mat/0005492, 29 May 2000. http://arxiv.org/abs/cond-mat/0005492.
• Sénéchal, D. ‘An Introduction to Bosonization’. arXiv:cond-mat/9908262, 18 August 1999. http://arxiv.org/abs/cond-mat/9908262.
• Von Delft, Jan, and Herbert Schoeller. ‘Bosonization for Beginners --- Refermionization for Experts’. Annalen Der Physik 7, no. 4 (November 1998): 225–305. doi:10.1002/(SICI)1521-3889(199811)7:4<225::AID-ANDP225>3.0.CO;2-L.
• Edward Frenkel, Free Field Realizations in Representation Theory, http://www.mathunion.org/ICM/ICM1994.2/Main/icm1994.2.1256.1269.ocr.pdf

articles

• Langmann, Edwin, and Per Moosavi. ‘Construction by Bosonization of a Fermion-Phonon Model’. arXiv:1503.01835 [math-Ph], 5 March 2015. http://arxiv.org/abs/1503.01835.
• Frenkel, E., and D. Gaitsgory. “Geometric Realizations of Wakimoto Modules at the Critical Level.” arXiv:math/0603524, March 21, 2006. http://arxiv.org/abs/math/0603524.
• Dotsenko, Vl. S. “The Free Field Representation of the su(2) Conformal Field Theory.” Nuclear Physics B 338, no. 3 (July 16, 1990): 747–58. doi:10.1016/0550-3213(90)90649-X.