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Gauge coupling unification in the flipped $$E_8$$ GUT Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 K. V. Stepanyantz
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Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein–Gordon field Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 T. V. Dudnikova
Abstract We consider the Cauchy problem for the Hamiltonian system consisting of the Klein–Gordon field and an infinite harmonic crystal. The dynamics of the coupled system is translation-invariant with respect to the discrete subgroup \(\mathbb{Z}^d\) of \(\mathbb{R}^d\). The initial date is assumed to be a random function that is close to two spatially homogeneous (with respect to the subgroup \(\mathbb{Z}^d\))
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The structure of shift-invariant subspaces of Sobolev spaces Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 A. Aksentijević, S. Aleksić, S. Pilipović
Abstract We analyze shift-invariant spaces \(V_s\), subspaces of Sobolev spaces \(H^s(\mathbb{R}^n)\), \(s\in\mathbb{R}\), generated by a set of generators \(\varphi_i\), \(i\in I\), with \(I\) at most countable, by the use of range functions and characterize Bessel sequences, frames, and the Riesz basis of such spaces. We also describe \(V_s\) in terms of Gramians and their direct sum decompositions
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Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 M. O. Katanaev
Abstract On (pseudo)Riemannian manifolds of two and three dimensions, we list all metrics that admit a complete separation of variables in the Hamilton–Jacobi equation for geodesics. There are three different classes of separable metrics on two-dimensional surfaces. Three-dimensional manifolds admit six classes of separable metrics. Within each class, metrics are related by canonical transformations
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Bose gas modeling of the Schwarzschild black hole thermodynamics Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 I. Ya. Aref’eva, I. V. Volovich
Abstract Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of their entropy. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in \(D = 4\) space–time dimensions is provided by the analytic continuation of the entropy of Bose gas with a nonrelativistic one-particle energy
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Solution of the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives in statistical mechanics Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 Z. Korichi, A. Souigat, R. Bekhouche, M. T. Meftah
Abstract We solve the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives for systems exhibiting noninteger power laws in their Hamiltonians. Based on the fractional Liouville equation, we calculate the density function (DF) of a classical ideal gas. If the Riemann–Liouville derivative is used, the DF is a function depending on both the momentum \(p\) and the coordinate
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Lotka–Volterra model with mutations and generative adversarial networks Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 S. V. Kozyrev
Abstract A model of population genetics of the Lotka–Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace–Beltrami operator with a Fisher–Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the
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Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 N. M. Khatamov, N. N. Malikov
Abstract We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability
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Infinitely many rotating periodic solutions for damped vibration systems Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-27 K. Khachnaoui
Abstract We investigate a particular type of damped vibration systems that incorporate impulsive effects. The objective is to establish the existence and multiplicity of \(Q\)-rotating periodic solutions. To achieve this, the variational method and the fountain theorem, as presented by Bartsch, are used. The research builds upon recent findings and extends them by introducing notable enhancements.
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Multidimensional Zaremba problem for the $$p(\,\cdot\,)$$ -Laplace equation. A Boyarsky–Meyers estimate Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 Yu. A. Alkhutov, G. A. Chechkin
Abstract We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous \(p(\,\cdot\,)\)-Laplace equation with a variable exponent \(p\) having a logarithmic continuity modulus.
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Recent progress in the theory of functions of several complex variables and complex geometry Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 Xiangyu Zhou
Abstract We give a survey on recent progress on converses of \(L^2\) existence theorem and \(L^2\) extension theorem which are two main parts in \(L^2\)-theory, and their applications in getting criteria of Griffiths positivity and characterizations of Nakano positivity of (singular) Hermitian metrics of holomorphic vector bundles, as well as the strong openness property and stability property of multiplier
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On Dirichlet problem Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 A. K. Gushchin
Abstract During almost two centuries after the Gauss’ formulation of the Dirichlet problem for Laplace equation, many famous mathematicians devoted their studies to this subject and to its various generalizations. Many interesting and important results have been obtained, which become already classical ones. Our paper is an extended presentation of the author’s talk on the international conference
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Geometry and quasiclassical quantization of magnetic monopoles Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 I. A. Taimanov
Abstract We present the basic physical and mathematical ideas (P. Curie, Darboux, Poincaré, Dirac) that led to the concept of magnetic charge, the general construction of magnetic Laplacians for magnetic monopoles on Riemannian manifolds, and the results of Kordyukov and the author on the quasiclassical approximation for eigensections of these operators.
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On the combination of Lebesgue and Riemann integrals in theory of convolution equations Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 N. B. Engibaryan
Abstract Using the example of scalar and vector Wiener–Hopf equations, we consider two methods for combining the options for the Riemann integral and Lebesgue functional spaces in problems of studying and solving integral convolution equations. The method of nonlinear factorization equations and the kernel averaging method are used. A generalization of the direct Riemann integrability is introduced
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A characterization of Gibbs semigroups Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 V. A. Zagrebnov, B. Iochum
Abstract We propose a new characterization of Gibbs semigroups, which is an extension of a similar characterization for compact semigroups.
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Ternary $$Z_3$$ -symmetric algebra and generalized quantum oscillators Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 R. Kerner
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Some new methods for studying boundary value problems for general partial differential equations Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01 V. P. Burskii
Abstract We consider methods for studying boundary value problems for linear partial differential equations in a domain regardless of the type of the equation. We propose several methods for studying boundary value problems, typically based on the Green’s formula. Our previous publications were devoted to these methods, and we present these results in a summarized form in this paper.
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Unitary representation of walks along random vector fields and the Kolmogorov–Fokker–Planck equation in a Hilbert space Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01
Abstract Random Hamiltonian flows in an infinite-dimensional phase space is represented by random unitary groups in a Hilbert space. For this, the phase space is equipped with a measure that is invariant under a group of symplectomorphisms. The obtained representation of random flows allows applying the Chernoff averaging technique to random processes with values in the group of nonlinear operators
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Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems Theor. Math. Phys. (IF 1.0) Pub Date : 2024-02-01
Abstract We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to
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Existence of an entropic solution of a nonlinear elliptic problem in an unbounded domain Theor. Math. Phys. (IF 1.0) Pub Date : 2024-01-01
Abstract We consider a second-order quasilinear elliptic equation with an integrable right-hand side. We formulate constraints on the structure of the equation in terms of a generalized \(N\) -function. We prove the existence of an entropic solution of the Dirichlet problem in nonreflexive Musielak–Orlicz–Sobolev spaces in an arbitrary unbounded strictly Lipschitz domain.
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Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side Theor. Math. Phys. (IF 1.0) Pub Date : 2024-01-01
Abstract A model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit absorption principle, a Lagrangian surface naturally appears that has a logarithmic singularity at one point. Because of this singularity, the solution is localized not only in a neighborhood of the projection of the Lagrangian surface onto the coordinate space
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On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations Theor. Math. Phys. (IF 1.0) Pub Date : 2024-01-01
Abstract For a system of nonlinear integral equations on the semiaxis, we study a boundary value problem whose matrix kernel has unit spectral radius. This boundary value problem has applications in various areas of physics and biology. In particular, such problems arise in the dynamical theory of \(p\) -adic strings for the scalar field of tachyons, in the mathematical theory of spread of epidemic
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On the quarkyonic phase in the holographic approach Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 I. Ya. Aref’eva
Abstract We study the problem of the existence of the quarkyonic phase in quantum chromodynamics. This phase can exists under certain conditions in quantum chromodynamics along with the phase of free quarks and the confinement phase. As is known, the confinement phase is characterized by the presence of a linear potential between quarks, and the quarks are confined to one hadron (meson or baryon).
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The structure of quantum corrections and exact results in supersymmetric theories from the higher covariant derivative regularization Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 K. V. Stepanyantz
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Nonexplicit versions of integrable equations Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 A. K. Pogrebkov
Abstract We consider some generalizations of a \((2+1)\)-dimensional Davey–Stewartson-type equation. In particular, we propose a dynamical system that does not admit an explicit formulation in terms of differential equations, but needs an additional independent variable.
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Comments on a 4-derivative scalar theory in 4 dimensions Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 A. A. Tseytlin
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A new solvable two-matrix model and the BKP tau function Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 E. N. Antonov, A. Yu. Orlov
Abstract We present exactly solvable modifications of the two-matrix Zinn-Justin–Zuber model and write it as a tau function. The grand partition function of these matrix integrals is written as the fermion expectation value. The perturbation theory series is written explicitly in terms of a series in strict partitions. The related string equations are presented.
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Cluster variables for affine Lie–Poisson systems Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 L. O. Chekhov
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Novel integrability in string theory from automorphic symmetries Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 A. V. Pribytok
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Violation of the $$T$$ invariance in the probabilities of spin–flavor transitions of neutrino characterized by a real mixing matrix Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 A. V. Chukhnova
Abstract We study the simultaneous interaction of a neutrino with matter and the electromagnetic field in the two-flavor model. We show that \(T\)-invariance violating terms can appear in the probabilities of not only spin-flip transitions but also flavor transitions between states with the same helicity in the case of the interaction via charged currents.
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On Poincaré–Birkhoff–Witt basis of the quantum general linear superalgebra Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 A. V. Razumov
Abstract We give a detailed derivation of the commutation relations for the Poincaré–Birkhoff–Witt generators of the quantum superalgebra \(\mathrm U_q(\mathfrak{gl}_{M|N})\).
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Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 G. Kulkarni, N. A. Slavnov
Abstract We consider an \(XYZ\) spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as linear combinations of new Bethe vectors. We also compute the multiple action of the gauge-transformed monodromy matrix elements on the pre-Bethe vector and express the results in terms of the partition function of the \(8\)-vertex
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Sigma models as Gross–Neveu models. II Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-22 D. V. Bykov
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Quantum corrections to the effective potential in nonrenormalizable theories Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-01
Abstract For the effective potential in the leading logarithmic approximation, we construct a renormalization group equation that holds for arbitrary scalar field theories, including nonrenormalizable ones, in four dimensions. This equation reduces to the usual renormalization group equation with a one-loop beta-function in the renormalizable case. The solution of this equation sums up the leading
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A new stability equation for the Abelian Higgs–Kibble model with a dimension-6 derivative operator Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-01
Abstract We show that the dynamics of the scalar Higgs field in the Abelian Higgs–Kibble model supplemented with a dimension-6 derivative operator can be constrained at the quantum level by a certain stability equation. It holds in the Landau gauge and is derived within the recently proposed extended field formalism, where the physical scalar is described by a gauge-invariant field variable. Physical
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Resonance fluorescence of polar quantum systems in a bichromatic field Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-01
Abstract We study spectral properties of fluorescent radiation from a two-level quantum system with broken inversion spatial symmetry, which can be implemented as a model of a one-electron two-level atom whose electric dipole moment operator has permanent unequal diagonal matrix elements. We consider the case of the excitation of this system by a bichromatic laser field consisting of a high-frequency
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Higher spins in harmonic superspace Theor. Math. Phys. (IF 1.0) Pub Date : 2023-12-01
Abstract We report on a recent progress in constructing off-shell \(4\) D, \(\mathcal{N}=2\) supersymmetric integer higher-superspin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with matter hypermultiplets. For even superspins, a new equivalent representation of the hypermultiplet couplings in terms of an analytic \(\omega\) superfield is presented
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Classification of semidiscrete equations of hyperbolic type. The case of third-order symmetries Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 R. N. Garifullin
Abstract We classify semidiscrete equations of hyperbolic type. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\biggl(\frac{du_{n}}{dx},u_{n+1},u_{n}\biggr),$$ where the unknown function \(u_n(x)\) depends on one discrete (\(n\)) and one continuous (\(x\)) variables. The classification is based on the requirement that generalized symmetries exist in the discrete and continuous directions
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$$T\overline T$$ deformation of the Calogero–Sutherland model via dimensional reduction Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 D. V. Pavshinkin
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Tau-function of the B-Toda hierarchy Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 V. V. Prokofev, A. V. Zabrodin
Abstract We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B), which can be regarded as a discretization of the BKP hierarchy. We introduce the tau function of the B-Toda hierarchy and obtain bilinear equations for it. Examples of soliton tau functions are presented in explicit form.
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On the scattering problem for a potential decreasing as the inverse square of distance Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 V. A. Gradusov, S. L. Yakovlev
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Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 M. O. Korpusov, A. Yu. Perlov, A. V. Timoshenko, R. S. Shafir
Abstract A system of equations with a quadratic nonlinearity in the electric field potential and temperature is proposed to describe the process of heating of semiconductor elements of an electrical board, with the thermal and electrical “breakdowns” possible in the course of time. For this system of equations, the existence of a classical solution not extendable in time is proved and sufficient conditions
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Integration of negative-order modified Korteweg–de Vries equation in a class of periodic functions Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 G. U. Urazboev, A. B. Yakhshimuratov, M. M. Khasanov
Abstract We study the negative-order modified Korteweg–de Vries equation and show that it can be integrated by the inverse spectral transform method. We determine the evolution of the spectral data for the Dirac operator with periodic potential associated with a solution of the negative-order modified Korteweg–de Vries equation. The obtained results allow applying the inverse spectral transform method
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Dirac representation of the $$SO(3,2)$$ group and the Landau problem Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 S. C. Tiwari
Abstract By systematically studying the infinite degeneracy and constants of motion in the Landau problem, we obtain a central extension of the Euclidean group in two dimension as a dynamical symmetry group, and \(Sp(2,\mathbb{R})\) as the spectrum generating group, irrespective of the choice of the gauge. The method of group contraction plays an important role. Dirac’s remarkable representation of
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$$\mathcal S$$ -modular transformation of the $$\mathcal N=2$$ superconformal algebra characters Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 M. R. Bahraminasab, M. Ghominejad
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On Bäcklund transformations for some second-order nonlinear differential equations Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 V. V. Tsegel’nik
Abstract We obtain second-order nonlinear differential equations (and the associated Bäcklund transformations) with an arbitrary analytic function of the independent variable. These equations (which are not of Painlevé type in general) under certain constraints imposed on an arbitrary analytic function can be reduced, in particular, to the second, third or fourth Painlevé equation. We consider the
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The impact of the Wiener process on solutions of the potential Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 F. M. Al-Askar
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Bases and interbasis expansions in the generalized MIC–Kepler problem in the continuous spectrum and the scattering problem Theor. Math. Phys. (IF 1.0) Pub Date : 2023-11-24 L. G. Mardoyan
Abstract The spherical and parabolic wave functions are calculated for the generalized MIC–Kepler system in the continuous spectrum. It is shown that the coefficients of the parabola–sphere and sphere–parabola expansion are expressed in terms of the generalized hypergeometric function \(_{3}F_2(\ldots\mid 1)\). The quantum mechanical problem of scattering in the generalized MIC–Kepler system is solved
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Scalar products of Bethe vectors in the generalized algebraic Bethe ansatz Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 G. Kulkarni, N. A. Slavnov
Abstract We consider an \(XYZ\) spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions, we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors.
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Revised Riemann–Hilbert problem for the derivative nonlinear Schrödinger equation: Vanishing boundary condition Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 Yongshuai Zhang, Haibing Wu, Deqin Qiu
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Entangled states in a simple model of quantum electrodynamics Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 Yu. M. Pismak
Abstract We consider the model of propagation of two particles created at one space point with correlated polarizations. Physical peculiarities of this process described in the framework of quantum electrodynamics are discussed in the context of quantum informatics.
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Two-photon production of dileptons at the LHC with electroweak corrections taken into account Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 V. A. Zykunov
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A generalized Crewther relation and the V scheme: analytic results in fourth-order perturbative QCD and QED Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 A. L. Kataev, V. S. Molokoedov
Abstract Using the analytic \(\overline{\mathrm{MS}}\) scheme, three-loop contribution to the perturbative Coulomb-like part of the static color potential of a heavy quark–antiquark system, we obtain an analytic expression for the fourth-order \(\beta\)-function in the gauge-invariant effective V scheme in the case of the generic simple gauge group. We also present the Adler function of electron–positron
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Two-species reaction–diffusion system in the presence of random velocity fluctuations Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 M. Hnatič, M. Kecer, T. Lučivjanský
Abstract We study random velocity effects on a two-species reaction–diffusion system consisting of three reaction processes \(A+A\to(\varnothing,A)\), \(A+B\to A\). Using the field theory perturbative renormalization group, we analyze this system in the vicinity of its upper critical dimension \(d_{\mathrm c}=2\). A velocity ensemble is generated by means of stochastic Navier–Stokes equations. In particular
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Noether charge, thermodynamics and phase transition of a black hole in the Schwarzschild– anti-de Sitter–Beltrami spacetime Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 T. Angsachon, K. Ruenearom
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Lie group geometry. Invariant metrics and dynamical systems, dual algebra, and their applications in the group analysis of a one-dimensional kinetic equation Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 A. V. Borovskikh
Abstract On a Lie group, we introduce a family of group-invariant metrics and show that the curves invariant under this group are spirals in all the introduced metrics (i.e., they have constant curvatures). An important role is played by an algebra, which we call dual, defined on the same group. The main relation between these algebras is that the trajectories of the one-parameter groups generated
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On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 I. T. Habibullin, A. R. Khakimova
Abstract We continue describing integrable nonlinear chains of the form \(u^j_{n+1,x}=u^j_{n,x}+f(u^{j+1}_{n},u^{j}_n,u^j_{n+1 },u^{j-1}_{n+1})\) with three independent variables on the basis of the existence of a hierarchy of Darboux-integrable reductions. The classification algorithm is based on the well-known fact that characteristic algebras of Darboux-integrable systems have a finite dimension
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Scaling violation and the appearance of mass in scalar quantum field theories Theor. Math. Phys. (IF 1.0) Pub Date : 2023-10-24 A. L. Pismensky, Yu. M. Pismak
Abstract In massless quantum field theories, scale invariance is violated in logarithmic dimensions. We discuss options for interpreting this effect as spontaneous mass emergence in the framework of skeleton self-consistency equations with the full propagator in the \(\varphi^3\), \(\varphi^4\), and \(\varphi^6\) models of a scalar field \(\varphi\).
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Strongly intensive variable in the model of high-energy pp interactions with the formation of string clusters Theor. Math. Phys. (IF 1.0) Pub Date : 2023-09-24 V. V. Vechernin, S. N. Belokurova
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Conformal invariance and phenomenology of particle creation: Weyl geometry vs. Riemannian geometry Theor. Math. Phys. (IF 1.0) Pub Date : 2023-09-24 V. A. Berezin, I. D. Ivanova
Abstract Using the example of an action for an ideal fluid with a variable number of particles, we study a phenomenological description of the processes of particle production in the background of strong external fields, including gravity and scalar fields. This model is discussed for Weyl geometry and Riemannian geometry. A new invariant related to the interaction of the Weyl vector with particles