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Feynman checkers: lattice quantum field theory with real time
Analysis and Mathematical Physics. 2024. Vol. 14. Article 38.
Skopenkov M., Ustinov A.
We present a new completely elementary model that describes the creation, annihilation, and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names
Feynman checkers or one-dimensional quantum walk. It can be viewed as a six-vertex model with certain complex weights of the vertices. The discrete model is consistent with the continuum quantum field theory, namely, reproduces the known expected charge density as the lattice step tends to zero. It is exactly solvable in terms of hypergeometric functions. We introduce interaction resembling Fermi's theory and establish perturbation expansion.
Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58
В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862
Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 844–854
Improving image quality is becoming an increasingly popular task, especially when working with mobile devices. One common approach to image enhancement is the use of convolutional neural networks. However, to achieve good results, such networks must be large enough, otherwise there is a risk of unwanted artifacts. In addition, large convolutional neural networks require significant ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Optical Memory and Neural Networks (Information Optics) 2024 Vol. 33 P. 424–434
This study explores the development of classifiers for microbial images, specifically focusing on streptococci captured via microscopy of live samples. Our approach uses AutoML-based techniques and automates the creation and analysis of feature spaces to produce optimal descriptors for classifying these microscopic images. This technique leverages interpretable taxonomic features based on the external geometric attributes ...
Added: September 21, 2026
Aleksei Samarin, Aleksei Toropov, Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1053–1060
This paper presents a novel approach to classification in biomedical imaging, specifically targeting polyp recognition in video endoscopy snapshots. Our method leverages specialized image descriptors to enhance the accuracy and robustness of polyp recognition. By employing these specialized descriptors, we address the challenges inherent in analyzing biomedical images from open datasets. Our approach not only ...
Added: September 21, 2026
Самарин А. В., Торопов А. Г., Савельев А. Г. et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 4 P. 1044–1052
This paper presents a study aimed at improving the detection quality of small-sized microorganisms under challenging microscopic conditions through the application of a lightweight combined image preprocessing model. We focused on the task of detecting diplococci in images obtained through dynamic sample microscopy. The proposed approach employs predefined filters for image preprocessing, combined with the ...
Added: September 21, 2026
Singapore: Springer Singapore, 2025.
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., / Series arXiv "math". 2025. No. 2511.20141.
This paper presents a novel approach to neural network compression that addresses redundancy at both the filter and architectural levels through a unified framework grounded in information flow analysis. Building on the concept of tensor flow divergence, which quantifies how information is transformed across network layers, we develop a two-stage optimization process. The first stage ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2009 Т. 424 № 5 С. 591–593
В данной статье вводится определенный класс дифференциальных уравнений с переменными коэффициентами, который тесно связан с операцией умножения Адамара и операторами Данкла имеющими применение в математической физике. Показано, что уравнения этого класса могут быть сведены к уранвениям в обобщенных производных с постоянными коэффициентами. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 169–178
This study explores the incorporation of specialized self-attention mechanisms into deep learning architectures, with a particular emphasis on segmenting human iris and pupil regions in infrared images. In this work, we present some modified versions of nonlocal blocks designed to enhance self-attentive properties while addressing the distinct characteristics of infrared imaging data. By applying these customized ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 10 Article 359
Timely identification and accurate delineation of ultra-early ischemic stroke lesions in non-contrast computed tomography (CT) scans of the human brain are of paramount importance for prompt medical intervention and improved patient outcomes. In this study, we propose a deep learning-driven methodology specifically designed for segmenting ultra-early ischemic regions, with a particular emphasis on both the ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., «Doklady Mathematics» 2012 Т. 443 № 3 С. 293–295
В данной работе введены обобщенные частные производные, изучены дифференциальные уравнения в обобщенных частных производных с постоянными коэффициентами и доказан фундаментальный принцип Эйлера для таких уравнений. Устанавливлена связь с классом уравнений в обычных частных производных с переменными коэффициентами. ...
Added: September 21, 2026
Springer, Cham, 2025.
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Journal of Imaging 2025 Vol. 11 No. 6 P. 1–20
This study presents a unified low-parameter approach to multi-class classification of microorganisms (micrococci, diplococci, streptococci, and bacilli) based on automated machine learning. The method is designed to produce interpretable taxonomic descriptors through analysis of the external geometric characteristics of microorganisms, including cell shape, colony organization, and dynamic behavior in unfixed microscopic scenes. A key advantage ...
Added: September 21, 2026
Shilov A. L., Elesin L., Kravtsov M. et al., Nature Communications 2026 Vol. 17 No. 1 Article 9734
Identifying the microscopic processes limiting conductivity is essential for understanding correlated quantum materials. In twisted bilayer graphene, metallic resistivity follows ρ ~ Tα with widely varying α, fueling competing interpretations from phonon-limited transport and umklapp scattering to strange metallicity and heavy-fermion renormalization. Here, we use terahertz excitation to selectively heat electrons while keeping the lattice cold, separating ...
Added: September 20, 2026
Medvedev V., Annals of Global Analysis and Geometry 2026 Vol. 70 No. 2 P. 8–23
This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 323–334
In this paper, an improved approach for automatic wildlife detection in natural environments based on the integration of a neural network architecture with a two-stream attention mechanism and a novel preclassification step based on infrared data has been presented. The proposed method addresses one of the key challenges in environmental monitoring: the need for scalable ...
Added: September 19, 2026
Sofia Rumyantseva, Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 Article 5
This paper investigates the Lorentz invariance of the multidimensional Dirac–Hestenes equation, that is, whether the equation remains form-invariant under pseudo-orthogonal transformations of the coordinates. We examine two distinct approaches: the tensor formulation and the spinor formulation. We first present a detailed examination of the four-dimensional Dirac–Hestenes equation, comparing both transformation approaches. These results are subsequently ...
Added: December 19, 2025
Sofia Rumyantseva, Shirokov D., Advances in Applied Clifford Algebras 2025 Vol. 35 Article 24
It is easier to investigate phenomena in particle physics geometrically by exploring a real solution to the Dirac-Hestenes equation instead of a complex solution to the Dirac equation. The present research outlines the multidimensional Dirac-Hestenes equation. Since the matrix representation of the complexified (Clifford) geometric algebra ℂ⊗Cℓ1,n depends on a parity of n, we explore even and odd ...
Added: November 8, 2024
Fedor Ozhegov, Reviews in Mathematical Physics 2024 Vol. 36 No. 7 Article 2450017
In this paper, we study Feynman checkers, one of the most elementary models of electron motion. It is also known as a one-dimensional quantum walk or an Ising model at an imaginary temperature. We add the simplest non-trivial electromagnetic field and find the limits of the resulting model for small lattice step and large time, ...
Added: May 17, 2024
Marchuk N., М.: Издательская группа URSS, 2023.
В книге изучаются релятивистские уравнения теории поля, в частности рассматриваются свойства ковариантности и симметрии уравнений Дирака—Максвелла и Дирака—Янга—Миллса. Вводится ряд новых систем уравнений, называемых модельными уравнениями теории поля. Эти системы уравнений воспроизводят основные свойства стандартных систем уравнений теории поля. В то же время модельные уравнения имеют ряд отличий от стандартных уравнений теории поля, в частности обладают новой внутренней симметрией ...
Added: January 3, 2024
Chetverikov V., Mamsurov I., , in: Proceedings of 2022 IEEE Moscow Workshop on Electronic and Networking Technologies (MWENT).: M.: IEEE, 2022. P. 1–4.
The solutions of the Schrodinger (Schrodinger – Pauli) equations and the Dirac equation in the 2+1 space for the two-dimensional motion of a charged particle in a uniform and constant magnetic field, as well as the construction of coherent states based on the solutions obtained are considered. A specific feature of this problem is the ...
Added: October 25, 2022
Skopenkov M., Ustinov A., / Cornell University. Серия arXiv "math". 2022.
We present a new completely elementary model which describes creation, annihilation and motion of non-interacting electrons and positrons along a line. It is a modification of the model known under the names Feynman checkers, or one-dimensional quantum walk, or Ising model at imaginary temperature. The discrete model is consistent with the continuum quantum field theory, ...
Added: October 23, 2022
М. Б. Скопенков, А. В. Устинов, Успехи математических наук 2022 Т. 77 № 3(465) С. 73–160
We survey and develop the most elementary model of electron motion introduced by R.Feynman. In this game, a checker moves on a checkerboard by simple rules, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk or an Ising model at imaginary temperature. We solve mathematically a problem by R.Feynman ...
Added: August 12, 2022