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TMF, 2006, Volume 146, Number 2, Pages 251–266 (Mi tmf2034)  

This article is cited in 1 scientific paper (total in 1 paper)

Renormalization-Group Transformation in a $2n$-Component Fermionic Hierarchical Model

R. G. Stepanov

Kazan State University

Abstract: We study the $2N$-component fermionic model on a hierarchical lattice and give explicit formulas for the renormalization-group transformation in the space of coefficients that determine a Grassmann-valued density of the free measure. We evaluate the inverse renormalization-group transformation. The de.nition of the renormalization-group fixed points reduces to a solution of a system of algebraic equations. We investigate solutions of this system for $N=1,2,3$. For $\alpha=1$, we prove an analogue of the central limit theorem for fermionic $2N$-component fields. We discover an interesting relation between renormalization-group transformations in bosonic and fermionic hierarchical models and show that one of these transformations is obtained from the other by replacing $N$ with $-N$.

Keywords: renormalization group, $N$-component fermionic fields, hierarchical models

DOI: https://doi.org/10.4213/tmf2034

Full text: PDF file (243 kB)
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English version:
Theoretical and Mathematical Physics, 2006, 146:2, 207–220

Bibliographic databases:

Received: 08.02.2005

Citation: R. G. Stepanov, “Renormalization-Group Transformation in a $2n$-Component Fermionic Hierarchical Model”, TMF, 146:2 (2006), 251–266; Theoret. and Math. Phys., 146:2 (2006), 207–220

Citation in format AMSBIB
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\paper Renormalization-Group Transformation in a~$2n$-Component Fermionic Hierarchical Model
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\jour Theoret. and Math. Phys.
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\pages 207--220
\crossref{https://doi.org/10.1007/s11232-006-0019-3}
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  • http://mi.mathnet.ru/eng/tmf2034
  • https://doi.org/10.4213/tmf2034
  • http://mi.mathnet.ru/eng/tmf/v146/i2/p251

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 265 (2009), 229–234  mathnet  crossref  mathscinet  zmath  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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