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SIGMA 7 (2011), 022, 12 pages arXiv:0912.2135
https://doi.org/10.3842/SIGMA.2011.022
Beyond the Gaussian
Kazuyuki Fujii
Department of Mathematical Sciences, Yokohama City University, Yokohama, 236-0027 Japan
Received January 12, 2011, in final form February 28, 2011; Published online March 04, 2011
Abstract
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.
Key words:
non-Gaussian integral; renormalized integral; discriminant; cubic equation.
pdf (298 Kb)
tex (11 Kb)
References
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Beyond Gaussian: a comment,
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Introduction to integral discriminants,
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- Whittaker E.T., Watson G.N.,
A course of modern analysis,
Cambridge University Press, Cambridge, 1996.
- Satake I.,
Linear algebra,
Shokabo, Tokyo, 1989 (in Japanese).
- Fujii K.,
Beyond the Gaussian. II. Some applications, in progress.
- Morozov A., Shakirov Sh.,
New and old results in resultant theory,
Theoret. and Math. Phys. 163 (2010), 587-617,
arXiv:0911.5278.
- Dolotin V., Morozov A.,
Introduction to non-linear algebra,
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007,
hep-th/0609022.
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