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The Canonical Operator in Many-Particle Problems and Quantum Field Theory
Vol. 71.
De Gruyter, 2022.
Maslov, Victor P., Shvedov O.
Translator: A. Stoyanovsky, Shishkova M., A. Alimov
Editor of translation: Nazaikinskii V. E.
In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum field theory in the Hamiltonian formalism, which encounters additional difficulties related to the Stückelberg divergences and the Haag theorem. Asymptotic methods for solving pseudodifferential equations with small parameter multiplying the derivatives, as well as the asymptotic methods developed in the present monograph for solving problems in statistical physics and quantum field theory, can be considered from a unified viewpoint if one introduces the notion of abstract canonical operator. The book can be of interest for researchers – specialists in asymptotic methods, statistical physics, and quantum fi eld theory as well as for graduate and undergraduate students of these specialities.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Ozhegov R., Махлуф М., Goltsman G. et al., Инженерная физика 2026 № 8 С. 27–39
This paper investigates the theoretical limits of object detection within isotropic scattering media using single-photon lidar. Within a simplified model, we derive the fundamental relationship between the maximum attainable detection range and the required photon count per pulse. Two distinct limiting regimes are analyzed: the ballistic photon regime, which maintains high spatial resolution but necessitates ...
Added: October 8, 2026
Didenkulova E., Chugunov V., Didenkulova I., Wave Motion 2026 Vol. 147 Article 103787
This work presents a new analytical solution of the shallow water theory for cylindrical propagation of long tsunami-like waves in the basin of variable depth. Considered model cases are related to tsunami wave propagation from an asteroid fallen into the sea, or from underwater volcanic eruptions. The corresponding bottom geometries represent radially symmetric obstacles such ...
Added: October 8, 2026
Flamarion M., Didenkulova E., Pelinovsky E., Physics Letters A 2026 Vol. 598 Article 132218
In this letter, bipolar solitary wave interactions in the Schamel equation are revisited numerically. Two simulation settings are considered: repeated collisions in a periodic domain, and the interaction of a positive solitary wave with a train of negative polarity solitary waves of equal amplitude. In the first case, when the amplitudes are comparable, the larger ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Isaev T. F., Шаров А. Н., Журнал вычислительной математики и математической физики 2026 Т. 66 № 1 С. 83–93
Исследуются свойства оптических покрытий на основе использования упрощенного симулятора ошибок в толщинах слоев покрытий при их напылении. Обосновывается возможность такого подхода. Выводятся аналитические оценки среднеквадратичного значения нормы вектора ошибок и степени коррелированности ошибок в толщинах слоев покрытия. Изучается зависимость среднеквадратичного значения нормы вектора ошибок и свойств покрытия от уровня случайных ошибок в слоях. ...
Added: October 5, 2026
Осипова А. М., Пилипенко С. В., Novikov D. I. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 063522
We investigate the prospects for observing a specific spectral distortion of the cosmic microwave
background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of
galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent
measurement of the CMB anisotropy multipoles with l 1⁄4 1, 2, 3, allow the ...
Added: October 5, 2026
Krivorol V., [б.и.], 2025.
We review some recent developments in 1st order GLSM construction, or so-called Gross–Neveu formalism for sigma models. We recall the general idea behind this framework and describe a 1st order GLSM data from which the general generalized Gross–Neveu model can be constructed, using CP^1 sigma model as simplest example. Then, we formulate a general statement that ...
Added: December 26, 2025
Krivorol V., Быков Д. В., Letters in Mathematical Physics 2025 Vol. 115 No. 4 Article 85
We revisit the classical aspects of N=(2,2) supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross–Neveu (“first-order GLSM”) formalism. We reformulate these models for complex Grassmannians in terms of simple supersymmetric Lagrangians with polynomial interactions. For maximal isotropic Grassmannians we propose two types of equivalent Lagrangians, which make either supersymmetry or the geometry ...
Added: December 26, 2025
Krivorol V., Быков Д. В., Advances in Theoretical and Mathematical Physics 2024 Vol. 28 No. 3 P. 1027–1079
We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop β-functions in this formalism, showing that they are proportional to the dual Coxeter numbers of the respective symmetry algebras. ...
Added: December 26, 2025
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2024 Vol. 110 No. 2 Article 025004
It has been shown that non-Abelian solitonic vortex string supported in four-dimensional (4D) N = 2
supersymmetric QCD (SQCD) with the U(2) gauge group and Nf =4 quark flavors becomes a critical
superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D space
and an internal space given by a Calabi-Yau noncompact threefold, ...
Added: September 20, 2024
A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2022 Vol. 106 No. 10 Article 106019
It has been shown that the non-Abelian solitonic vortex string supported in four-dimensional (4D)
N = 2 supersymmetric QCD (SQCD) with the U(2) gauge group and N_f = 4 quark flavors becomes a
critical superstring. This string propagates in the ten-dimensional space formed by a product of the flat 4D
space and an internal space given by a Calabi-Yau noncompact ...
Added: December 21, 2022
Gorsky A., E. Ievlev, A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 101 No. 1 Article 014013
We study the dynamics of non-Abelian vortex strings supported in N =2 supersymmetric QCD with
the U(N) gauge group and N_f = N quark flavors deformed by the mass μ of the adjoint matter. In the limit
of large μ the bulk four-dimensional theory flows to N = 1 supersymmetric QCD. The dynamics of
orientational zero modes of the non-Abelian string ...
Added: October 31, 2022
Chen J., Sheu C., Shifman M. et al., Journal of High Energy Physics 2020 Vol. 2020 No. 10 Article 59
We study two-dimensional weighted N = (2; 2) supersymmetric CP models
with the goal of exploring their infrared (IR) limit. WCP(N, tildeN) are simplifed versions
of world-sheet theories on non-Abelian strings in four-dimensional N = 2 QCD. In the
gauged linear sigma model (GLSM) formulation, WCP(N, tildeN) has N charges +1 and tilde N
charges -1 fields. As well-known, at e N ...
Added: October 31, 2022
E. Ievlev, Shifman M., A. Yung, Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 Vol. 102 No. 5 Article 054026
We study non-Abelian vortex strings in four-dimensional (4D) N = 2 supersymmetric QCD with the
U(2) gauge group and N_f =4 flavors of quark hypermultiplets. It has recently been shown that these
vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory
was found and interpreted as a spectrum of hadrons in 4D N ...
Added: October 31, 2022
S. Derkachov, Isaev A. P., Shumilov L., Physics Letters B 2022 Vol. 830 Article 137150
A convenient operator representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional “fishnet” field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag multi-loop two-point diagrams ...
Added: October 27, 2022