Editing Quantum Hall effect (section)

== Research status ==
The fractional quantum Hall effect  is considered part of ''exact quantization''.<ref>{{cite journal|journal=Science|title=In Praise of Exact Quantization|year=2010 |doi=10.1126/science.1194123 |url=https://www.science.org/doi/10.1126/science.1194123|last1=Franz |first1=Marcel |volume=329 |issue=5992 |pages=639–640 |pmid=20689008 |s2cid=206528413 |url-access=subscription }}</ref> Exact quantization in full generality is not completely understood but it has been explained as a very subtle manifestation of the combination of the principle of [[gauge invariance]] together with another symmetry (see [[Anomaly (physics)|Anomalies]]). The integer quantum Hall effect instead is considered a solved research problem<ref>{{cite web|title=Haldane nobel prize Lecture|url=https://www.nobelprize.org/uploads/2018/06/haldane-lecture-slides.pdf}}</ref><ref name=Laughlin:1981 /> and understood in the scope of [[TKNN formula]] and [[Chern–Simons theory|Chern–Simons Lagrangians]].

The [[fractional quantum Hall effect]] is still considered an open research problem.<ref name="Hansson 025005"/> The fractional quantum Hall effect can be also understood as an integer quantum Hall effect, although not of electrons but of charge–flux composites known as [[composite fermions]].<ref>{{cite book|first=Jain|last=Jainendra|title=Composite Fermions|date=19 April 2012 |publisher=Cambridge University Press|isbn=978-1107404250}}</ref> Other models to explain the fractional quantum Hall effect also exists.<ref>{{cite web|first=David|last=Tong|title=Quantum Hall Effect|url=http://www.damtp.cam.ac.uk/user/tong/qhe.html}}</ref>
Currently it is considered an open research problem because no single, confirmed and agreed list of fractional quantum numbers exists, neither a single agreed model to explain all of them, although there are such claims in the scope of [[composite fermions]] and Non Abelian [[Chern–Simons theory|Chern–Simons Lagrangians]].