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1.
M. D. Missarov R. G. Stepanov 《Proceedings of the Steklov Institute of Mathematics》2009,265(1):154-164
We reduce the calculation of the vertex parts of p-adic Feynman amplitudes to a recursive procedure for evaluating singular parts of certain integrals. We propose an algorithm for calculating these integrals in the general form. As an example, we consider vertex parts of amplitudes in the ? 4 theory. 相似文献
2.
M. D. Missarov 《Theoretical and Mathematical Physics》2012,173(3):1637-1643
We study the renormalization group action in a fermionic hierarchical model in the space of coefficients determining the Grassmann-valued density of the free measure. This space is interpreted as the two-dimensional projective space. The renormalization group map is a homogeneous quadratic map and has a special geometric property that allows describing invariant sets and the global dynamics in the whole space. 相似文献
3.
M. D. Missarov 《Theoretical and Mathematical Physics》1998,117(3):1483-1498
The dynamics of the renormalization-group transformation in the coupling-constant space of the fermionic hierarchical model
are discussed. The critical behavior of this model is described in terms of the complex behavior of the Grassmann-valued mean-spin
distribution density with the proper normalization. Some critical indices are calculated.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 471–488, December, 1998. 相似文献
4.
M. D. Missarov 《Letters in Mathematical Physics》1994,32(4):347-356
Discretization ofp-adic Grassmann-valued
-model leads to a hierarchical model with the Hamtilonian given by a nontrivial functional integral over the Grassmann variables. Using renormalization group arguments, we reduce the calculation of this integral to a functional equation. The problem of the convergence of the perturbation expansion of this integral, realized as a small-divisors problem, is investigated. 相似文献
5.
M. D. Missarov A. F. Shamsutdinov 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):211-221
The renormalization group dynamics is studied in the four-component fermionic hierarchical model in the space of coefficients that determine the Grassmann-valued density of the free measure. This space is treated as a two-dimensional projective space. If the renormalization group parameter is greater than 1, then the only attracting fixed point of the renormalization group transformation is defined by the density of the Grassmann δ-function. Two different invariant neighborhoods of this fixed point are described, and an algorithm is constructed that allows one to classify the points on the plane according to the way they tend to the fixed point. 相似文献
6.
The Gaussian part of the Hamiltonian of the four-component fermion model on a hierarchical lattice is invariant under the block-spin transformation of the renormalization group with a given degree of normalization (the renormalization group parameter). We describe the renormalization group transformation in the space of coefficients defining the Grassmann-valued density of a free measure as a homogeneous quadratic map. We interpret this space as a two-dimensional projective space and visualize it as a disk. If the renormalization group parameter is greater than the lattice dimension, then the unique attractive fixed point of the renormalization group is given by the density of the Grassmann delta function. This fixed point has two different (left and right) invariant neighborhoods. Based on this, we classify the points of the projective plane according to how they tend to the attracting point (on the left or right) under iterations of the map. We discuss the zone structure of the obtained regions and show that the global flow of the renormalization group is described simply in terms of this zone structure. 相似文献
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8.
M. D. Missarov 《Theoretical and Mathematical Physics》1996,109(1):1249-1259
The procedure of constructing the discrete approximation of p-adic 4-theory on a hierarchical lattice is reduced to the solution of an integral functional equation. The renormalization procedure and -functions are constructed in terms of this solution.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No 1, pp. 3–16, October, 1996. 相似文献
9.
We define fractional-dimensional p-adic Feynman amplitudes and construct a dimensional renormalization with minimum subtractions. In the fermionic model case, another dimensional renormalization procedure is defined as the inversion of the normalizing transformation at the trivial stable point for the hierarchical renormalization group transformation. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 462–475, June, 2000. 相似文献
10.
Russian Mathematics - The article describes a new type of Gaussian fields on a two-dimensional 2-adic space, invariant under the translation group and group of scaling transformations (self-similar... 相似文献