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Abstract <p>On a two-dimensional generalized hierarchical lattice, the distance between opposite vertices of a square unit cell differs from the distance between adjacent vertices and is a new parameter of model. At each vertex of the lattice, the field is given by a set of four components that are generators of a Grassmann algebra. The Gaussian part of the model is defined by a quadratic Hamiltonian that is invariant under the renormalization group transformation. The non-Gaussian part of the model is given by a Grassmann-valued “free measure density,” whose sets of coefficients are treated as points in a two-dimensional projective plane. The renormalization group transformation in the space of these coefficients is a homogeneous transformation of degree 4 in the projective space. The commutation relation between a Fourier transform in the space of “densities” and a renormalization group transformation is investigated.</p>

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On Fourier Transform and Renormalization Group Transformation in Generalized Fermionic Hierarchical Model

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • M. D. Missarov,
  • D. A. Khairullin

摘要

Abstract

On a two-dimensional generalized hierarchical lattice, the distance between opposite vertices of a square unit cell differs from the distance between adjacent vertices and is a new parameter of model. At each vertex of the lattice, the field is given by a set of four components that are generators of a Grassmann algebra. The Gaussian part of the model is defined by a quadratic Hamiltonian that is invariant under the renormalization group transformation. The non-Gaussian part of the model is given by a Grassmann-valued “free measure density,” whose sets of coefficients are treated as points in a two-dimensional projective plane. The renormalization group transformation in the space of these coefficients is a homogeneous transformation of degree 4 in the projective space. The commutation relation between a Fourier transform in the space of “densities” and a renormalization group transformation is investigated.