Beyond the Gaussian

In this paper we present a non-Gaussian integral based on a cubic polynomial, instead of a quadratic, and give a fundamental formula in terms of its discriminant. It gives a mathematical reinforcement to the recent result by Morozov and Shakirov. We also present some related results. This is simply...

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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2011-01, Vol.7, p.022
Main Author: Fujii, Kazuyuki
Format: Article
Language:English
Subjects:
cubic equation
discriminant
non-Gaussian integral
renormalized integral
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Summary:In this paper we present a non-Gaussian integral based on a cubic polynomial, instead of a quadratic, and give a fundamental formula in terms of its discriminant. It gives a mathematical reinforcement to the recent result by Morozov and Shakirov. We also present some related results. This is simply one modest step to go beyond the Gaussian but it already reveals many obstacles related with the big challenge of going further beyond the Gaussian.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2011.022