查看“︁高斯自由场”︁的源代码

在[[量子场论]]中，'''高斯自由场（Gaussian Free Field）'''是最简单的场论之一。这个也称为无质量[[玻色子]]场论。

== 介绍 ==
高斯自由场的[[泛函积分]]是

<math>Z = \int D\phi \exp(-\int_{R^d} d^dx \ \frac{1}{2}\phi^2 )</math>

<math>\phi</math>是'''高斯自由场'''。<math>\phi(x) = f(x)</math>的概率是

<math>P(\phi = f) = \frac{1}{Z} \exp(-\int \frac{1}{2}f^2 )</math>

== 属性 ==

* 高斯场论是一个[[共形场论]]
* 高斯场论描述一个无质量的[[玻色子]]
* <math>m=0</math>的[[Klein-Gordon场论]]
* <math>d=1</math>的高斯场论描述[[维纳过程]]

== 应用 ==

* [[随机矩阵]]
* [[随机漫步]]（[[格子]]）
* [[双体模型]]
* [[Schramm–Loewner演进]]

== 参考文献 ==

* Ding, J.; Lee, J. R.; Peres, Y. (2012), "Cover times, blanket times, and majorizing measures", ''Annals of Mathematics'', '''175''': 1409–1471, arXiv:1004.4371, doi:10.4007/annals.2012.175.3.8
* Dubédat, J. (2009), "SLE and the free field: Partition functions and couplings", ''J. Amer. Math. Soc.'', '''22''': 995–1054, arXiv:0712.3018, Bibcode:2009JAMS...22..995D, doi:10.1090/s0894-0347-09-00636-5
* Kenyon, R. (2001), "Dominos and the Gaussian free field", ''Annals of Probability'', '''29''' (3): 1128–1137, arXiv:math-ph/0002027, doi:10.1214/aop/1015345599, MR 1872739
* Peres, Y. (2001), "An Invitation to Sample Paths of Brownian Motion" (PDF), ''Lecture notes at UC Berkeley''
* Rider, B.; Virág, B. (2007), "The noise in the Circular Law and the Gaussian Free Field", ''International Mathematics Research Notices'': article ID rnm006, 32 pages, MR 2361453
* Sheffield, S. (2005), "Local sets of the Gaussian Free Field", ''Talks at the Fields Institute, Toronto, on September 22–24, 2005, as part of the "Percolation, SLE, and related topics" Workshop.''
* Sheffield, S. (2007), "Gaussian free fields for mathematicians", ''Probability Theory and Related Fields'', '''139''': 521–541, arXiv:math.PR/0312099, doi:10.1007/s00440-006-0050-1, MR 2322706
* Friedli, S.; Velenik, Y. (2017). ''Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction''. Cambridge: Cambridge University Press. ISBN <bdi>9781107184824</bdi>.

[[Category:量子场论]]