1995/07/06 by Olivier de Mirleau, de Mirleau, Olivier
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9507039
61 pages amslatex. Uses amssym and amssym.def
arxiv created 1995/07/06 · openalex publication_date 1995/07/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we present a number of generalizations of Wick's theorems on integrals with Gaussian weight to a larger class of weights which we call subgaussian. Examples of subgaussian contractions are that of Kac-Moody or Virasoro type, although the concept of a subgaussian weight does not refer a priori to two-dimensional field theory. The generalization was chosen in such a way that the contraction rules become a combinatorical way of solving the Schwinger-Dyson equation. In a still more general setting we prove a relation between solutions of the Schwinger-Dyson equation and a map N, which in the Gaussian case reduces to normal ordering. Furthermore, we give a number of results concerning contractions of composite insertions, which do not suffer from the Johnson-Low problem of ``commutation'' relations that do not satisfy the Jacobi identity.