arXiv subjects

Olivier de Mirleau

Publications and source records attributed to Olivier de Mirleau.

3 recordsLinked to original sources

arXiv1997

Further illustration of the use of the Frobenius-Schwinger-Dyson equations

The Frobenius-Schwinger-Dyson equations are a rather high-brow abstract nonsense type of equations describing n-point functions of arbitrarily high composite insertions. It is not clear how to solve or even find approximate solutions of these equations in general, but they are worth investigating because (a certain preferred type of) renormalization of composite insertions has been performed in advance: it just remains to find solutions given an action and renormalization conditions. Earlier work in this field involved only Gaussian actions or variable transformations thereof. In this work we illustrate the use of Frobenius-Schwinger-Dyson at a less obviously trivial level, that of the Thirring model.

hep-th↗

arXiv1996

Concerning a natural compatibility condition between the action and the renormalized operator product

In this article we note that in a number of situations the operator product and the classical action satisfy a natural compatibility condition. We consider the interest of this condition to be twofold: First, the naturality (functoriality) of the compatibility condition suggests that it be used for geometrical applications of renormalized functional integration. Second, the compatibility can be used as the definition of a category; consideration of this category as the central object of study in quantum field theory seems to have quite some advantages over previously introduced theories of the type ``S-matrix theory'', ``Vertex operator algebras'', since this seems to be the only category in which both the action and the expectation values enter, the two being linked roughly speaking by a combination of the Frobenius property and the renormalized Schwinger-Dyson equation.

hep-th↗

arXiv1995

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

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.

hep-th↗