We provide a concise introduction to the basic properties of Gaussian integration. These include Gaussian integration by parts, the connection with the Laplace operator, Wick’s lemma, the characterisation by the Laplace transform, and the computation of cumulants (also called truncated expectations). The fact that the sum of two independent Gaussian fields is also Gaussian is derived, along with the corresponding convolution property which is fundamental for the renormalisation group.
KeywordsGaussian integration Covariance Wick’s lemma Cumulants
- 38.D.C. Brydges, Lectures on the renormalisation group, in Statistical Mechanics, ed. by S. Sheffield, T. Spencer. IAS/Park City Mathematics Series, vol. 16 (American Mathematical Society, Providence, 2009), pp. 7–93Google Scholar