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In [[theoretical physics|theoretical]] [[condensed matter physics]], '''Bosonization''' is a mathematical procedure by which a system of interacting [[fermions]] in [[dimension|(1+1) dimensions]] can be transformed to a system of massless, non-interacting [[bosons]].<ref name=gogolin>{{cite book|last=Gogolin|first=Alexander O.|title=Bosonization and Strongly Correlated Systems|year=2004|publisher=Cambridge University Press|isbn=0-521-61719-7|url=http://books.google.com/books?id=BZDfFIpCoaAC&dq=Bosonization+and+Strongly+Correlated+Systems&lr=&source=gbs_navlinks_s}}</ref> 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.<ref name=gogolin /> | |||
The basic physical idea behind bosonization is that [[Dirac sea|particle-hole excitations]] are bosonic in character. However, it was shown by [[Sin-Itiro Tomonaga|Tomonaga]] in 1950 that this principle is only valid in one-dimensional systems.<ref name=senechal>{{cite journal|last=Sénéchal|first=David|title=An Introduction to Bosonization|journal=Theoretical Methods for Strongly Correlated Electrons|year=1999|series=CRM Series in Mathematical Physics|doi=10.1007/0-387-21717-7_4|url=http://www.springerlink.com/content/q8p7094320733111/}}</ref> Bosonization is an [[effective field theory]] that focuses on low-energy excitations.<ref name=glazman>{{cite book|last=Sohn|first=Lydia (ed.)|title=Mesoscopic electron transport|year=1997|publisher=Springer|isbn=0-7923-4737-4|url=http://arxiv.org/pdf/cond-mat/9610037v1.pdf}}</ref> | |||
Two complex fermions <math>\psi,\bar\psi</math> are written as functions of a boson <math>\phi</math> | |||
:<math>\bar\psi_-\psi_+ = :\exp(i\phi):,\qquad \bar\psi_-\psi_+ = :\exp(-i\phi):</math><ref> | |||
In actuality, there is a [[cocycle]] prefactor to give correct (anti-)commutation relations with other fields under consideration.</ref> | |||
while the inverse map is given by | |||
:<math>\partial\phi=:\bar\psi\psi:</math> | |||
All equations are [[normal-order]]ed. The changed statistics arises from [[anomalous dimension]]s of the fields. | |||
==References== | |||
<references /> | |||
[[Category:Quantum field theory]] | |||
[[Category:Condensed matter physics]] | |||
{{quantum-stub}} | |||
Revision as of 17:44, 21 October 2013
In theoretical condensed matter 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.[1] 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.[1]
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.[2] Bosonization is an effective field theory that focuses on low-energy excitations.[3]
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.
References
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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ In actuality, there is a cocycle prefactor to give correct (anti-)commutation relations with other fields under consideration.