Abstract
We reduce the counting problem for the vacuum diagrams of a φ4 theory to a moment problem. As a consequence we are able to give the generating function for the counting of diagrams on a torus with one hole, besides the known result for planar diagrams. The method can be extended to φn theory and also to the counting of diagrams on a torus with an arbitrary number of holes.
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Brezin, E., Itzykson, C., Parisi, G., Zuber, J. B.: Planar diagrams. Commun. Math. Phys.59, 35–51 (1978)
Akhiezer, N. I.: The classical moment problem, p. 23. Oliver and Boyd 1965
Same as Ref. [2, p. 5]
Laguerre, E.: Sur la réduction en fractions continues d'une fonction qui satisfait à une équation différentielle linéaire du premier ordre dont les coefficients sont rationnels. J. Math.1, 135–165 (1885)
Same as Ref. [2, pp. 9, 10]
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Communicated by R. Stora
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Bessis, D. A new method in the combinatorics of the topological expansion. Commun.Math. Phys. 69, 147–163 (1979). https://doi.org/10.1007/BF01221445
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DOI: https://doi.org/10.1007/BF01221445