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Non-Gaussian generalizations of Wick's theorems, related to the Schwinger-Dyson equation

Olivier de Mirleau
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Abstract

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.

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Olivier de Mirleau. 1995-07-06. Non-Gaussian generalizations of Wick's theorems, related to the Schwinger-Dyson equation. https://arxiv.org/abs/hep-th/9507039

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