高斯自由场

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

是高斯自由场。的概率是

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
 的Klein-Gordon场论
 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 9781107184824.

量子场论