In theoretical condensed matter physics and particle physics, Bosonization is a mathematical procedure by which a system of interacting fermions in (1+1) 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 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
- Gogolin, Alexander O. (2004). Bosonization and Strongly Correlated Systems. Cambridge University Press. ISBN 0-521-61719-7.
- Coleman, S. (1975). "Quantum sine-Gordon equation as the massive Thirring model" Physical Review D11 2088; Witten, E. (1984). "Non-abelian bosonization in two dimensions", Communications in Mathematical Physics 92 455-472. online
- Sénéchal, David (1999). "An Introduction to Bosonization". Theoretical Methods for Strongly Correlated Electrons. CRM Series in Mathematical Physics. doi:10.1007/0-387-21717-7_4.
- Sohn, Lydia (ed.) (1997). Mesoscopic electron transport. Springer. arXiv: . ISBN 0-7923-4737-4.
- In actuality, there is a cocycle prefactor to give correct (anti-)commutation relations with other fields under consideration.
|This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.|