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 Tr. Mat. Inst. Steklova, 2004, Volume 245, Pages 172–181 (Mi tm183)

Symmetry of the Renormalization Group in $p$-Adic Models

M. D. Missarov

Kazan State University

Abstract: Bosonic and fermionic fields are considered on a ball in a $d$-dimensional $p$-adic space. These fields are defined by a Hamiltonian whose Gaussian part is invariant with respect to the Wilson renormalization group (RG) $R(\alpha)$ with parameter $\alpha$ and the non-Gaussian part is a formal series of finite-particle Hamiltonians. Let $F$ be a functional map applied only to the non-Gaussian part of $H$. A new symmetry of the renormalization group is defined by the commutator relation $R(\alpha )FH=FR(2d-\alpha )H$. As a consequence of this symmetry, the non-Gaussian branch of the stable points of the RG with $\alpha =d/2$ bifurcates from the fixed point corresponding to a constant (zero) random field.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 160–168

Bibliographic databases:

UDC: 519.248.2
Received in October 2003

Citation: M. D. Missarov, “Symmetry of the Renormalization Group in $p$-Adic Models”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 245, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 172–181; Proc. Steklov Inst. Math., 245 (2004), 160–168

Citation in format AMSBIB
\Bibitem{Mis04} \by M.~D.~Missarov \paper Symmetry of the Renormalization Group in $p$-Adic Models \inbook Selected topics of $p$-adic mathematical physics and analysis \bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov \serial Tr. Mat. Inst. Steklova \yr 2004 \vol 245 \pages 172--181 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm183} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099880} \zmath{https://zbmath.org/?q=an:1098.81069} \transl \jour Proc. Steklov Inst. Math. \yr 2004 \vol 245 \pages 160--168 

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This publication is cited in the following articles:
1. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84
2. M. D. Missarov, “Functional Fourier transformation and renormalization group transformation in bosonic field theory models”, Theoret. and Math. Phys., 174:2 (2013), 263–272
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