“Bosonization”的意思、由来-开放百科全书

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.

^[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] In particle physics, however, the boson is interacting, cf, the Sine-Gordon model, and notably through topological interactions,^[2] 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.^[3] Bosonization is an effective field theory that focuses on low-energy excitations.^[4] This is done for Luttinger liquid theory.

All equations are normal-ordered. The changed statistics arises from anomalous dimensions of the fields.

See also

References

1. ^¹{{cite book|last=Gogolin|first=Alexander O.|title=Bosonization and Strongly Correlated Systems|year=2004|publisher=Cambridge University Press|isbn=978-0-521-61719-2|url=https://books.google.com/books?id=BZDfFIpCoaAC&dq=Bosonization+and+Strongly+Correlated+Systems}}
2. ^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
3. ^{{Cite book|last=Sénéchal|first=David|title=An Introduction to Bosonization|journal=Theoretical Methods for Strongly Correlated Electrons|pages=139–186|year=1999|series=CRM Series in Mathematical Physics|doi=10.1007/0-387-21717-7_4|url=http://www.springerlink.com/content/q8p7094320733111/|arxiv=cond-mat/9908262|bibcode=2004tmsc.book..139S|isbn=978-0-387-00895-0}}
4. ^{{cite book|last=Sohn|first=Lydia (ed.)|title=Mesoscopic electron transport|pages=cond–mat/9610037|year=1997|publisher=Springer|isbn=978-0-7923-4737-8|arxiv=cond-mat/9610037|bibcode = 1996cond.mat.10037F }}
5. ^In actuality, there is a cocycle prefactor to give correct (anti-)commutation relations with other fields under consideration.