查看“︁拉廷格定理”︁的源代码

{{NoteTA|G1=物理學}}

[[File:Fermi_Surface.svg|右|缩略图|200x200像素|拉廷格定理将费米液体的粒子密度与其费米面包括的体积联系了起来。]]

'''拉廷格定理'''是[[凝聚态物理学]]的电子输运领域的一个具有广泛意义的结论，于1960年由{{le|华金·马萨达克·拉廷格|Joaquin Mazdak Luttinger|J·M·拉廷格}}和{{le|约翰·克莱夫·沃德|John Clive Ward|J·C·沃德}}提出。<ref>
{{Cite journal|title=Ground-State Energy of a Many-Fermion System. II|last=Luttinger, J. M.|last2=Ward, J. C.|journal=Physical Review|issue=5|doi=10.1103/PhysRev.118.1417|year=1960|volume=118|pages=1417–1427|bibcode=1960PhRv..118.1417L}}</ref><ref>
{{Cite journal|title=Fermi Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions|last=Luttinger|first=J. M.|journal=Physical Review|issue=4|doi=10.1103/PhysRev.119.1153|year=1960|volume=119|pages=1153–1163|bibcode=1960PhRv..119.1153L}}</ref> 它在电子关联的理论模型中经常出现，如[[高溫超導體]]，以及[[光电效应]]（金属的[[费米面]]可在其中被直接观测到）。

== 定义 ==
拉廷格定理表明，材料费米面所包含的体积和粒子密度呈正相关关系。

虽然该定理是[[泡利不相容原理]]对于非相互作用粒子的直接结论，但如果恰当地定义了费米面和粒子密度，在考虑粒子间相互作用时该定理也能成立，即费米面必须根据以下准则被定义：

: <math>G(\omega=0,\,p) \to 0</math> 或 <math>\infty,</math>

其中 <math>G</math> 为自变量为频率和动量的单粒子[[格林函數]]。于是，拉廷格定理可变形为以下形式<ref>
{{Cite book|last=Alexei M. Tsvelik|year=2003|title=Quantum Field Theory in Condensed Matter Physics|url=https://archive.org/details/quantumfieldtheo00tsve_281|edition=2nd|page=[https://archive.org/details/quantumfieldtheo00tsve_281/page/n346 327]|publisher=Cambridge University Press|isbn=978-0-521-82284-8}}</ref>：

: <math>n = 2 \int_{G(\omega=0,p)>0}\frac{d^D k}{(2\pi)^D}</math>

其中 <math>G</math> 与上面的定义一致，<math>d^D k</math> 表示在<math>D</math>-维<math>k</math>-空间的微分体积单元。

== 另见 ==

* [[朗道-费米液体理论]]
* [[费米面]]
* {{le|拉廷格-沃德泛函|Luttinger–Ward functional}}

== 参考资料 ==
{{Reflist}}

== 延伸阅读 ==
* {{cite journal |arxiv=1207.4201 |author1=Kiaran B. Dave|author2=Philip W. Phillips|author3=Charles L. Kane |title=Absence of Luttinger's theorem  |year=2012 |doi=10.1103/PhysRevLett.110.090403 |pmid=23496693|volume=110 |issue=9 |pages=090403|journal=Physical Review Letters |bibcode=2013PhRvL.110i0403D}}
* {{cite journal |author=M. Oshikawa |year=2000 |title=Topological Approach to Luttinger's Theorem and the Fermi Surface of a Kondo Lattice |journal=Physical Review Letters |volume=84 |issue=15 |pages=3370–3373 |doi=10.1103/PhysRevLett.84.3370|arxiv = cond-mat/0002392 |bibcode = 2000PhRvL..84.3370O |pmid=11019092}}
*{{Cite book<!-- Deny Citation Bot--> | title=Luttinger Model: The First 50 Years and Some New Directions |series=Series on Directions in Condensed Matter Physics |volume = 20| year=2013 | last1 = Mastropietro | first1 = Vieri | last2 = Mattis | first2 = Daniel C. | isbn = 978-981-4520-71-3|doi = 10.1142/8875|bibcode = 2013SDCMP..20.....M |publisher=World Scientific}}
*{{cite conference |author=F. D. M. Haldane |year=2005 |title=Luttinger's Theorem and Bosonization of the Fermi Surface |booktitle=Proceedings of the International School of Physics "Enrico Fermi", Course CXXI "Perspectives in Many-Particle Physics" |editors=R. A. Broglia and J. R. Schrieffer |publisher=North-Holland |pages=5–29 |arxiv=cond-mat/0505529|bibcode=2005cond.mat..5529H }}

[[Category:费米子]]
[[Category:凝聚体物理学]]