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Gauge coupling unification in the flipped $$E_8$$ GUT 翻转的 $$E_8$ GUT 中的量子耦合统一
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-27 DOI: 10.1134/s0040577924020090
K. V. Stepanyantz

Abstract

The gauge coupling unification is investigated at the classical level under the assumptions that the gauge symmetry breaking chain is (E_8to E_7times U_1 to E_6times U_1 to SO_{10}times U_1 to SU_5 times U_1 to SU_3 times SU_2 times U_1) and only components of the representations 248 of (E_8) can acquire vacuum expectation values. We demonstrate that there are several options for the relations between the gauge couplings of the resulting theory, but the only symmetry breaking pattern corresponds to (alpha_3=alpha_2) and (sin^2theta_mathrm{W}=3/8). Moreover, only for this option does the particle content of the resulting theory include all MSSM superfields. It is also noted that this symmetry breaking pattern corresponds to the case where all representation that acquire vacuum expectation values have the minimal absolute values of the relevant (U_1) charges.

摘要 我们在经典水平上研究了量规耦合统一，假设量规对称性破缺链是（E_8to E_7times U_1 to E_6times U_1 to SO_{10}times U_1 to SU_5 times U_1 to SU_3 times SU_2 times U_1），并且只有（E_8）的表示248的成分可以获得真空期望值。我们证明，由此产生的理论的规耦合之间的关系有几种选择，但是唯一的对称性破缺模式对应于(alpha_3=alpha_2)和(sin^2theta_mathrm{W}=3/8)。此外，只有在这个选项中，所得理论的粒子内容才包括所有的MSSM超场。我们还注意到，这种对称性破缺模式对应于所有获得真空期望值的表示都具有相关(U_1)电荷的最小绝对值的情况。
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引用次数: 0
On the combination of Lebesgue and Riemann integrals in theory of convolution equations 论卷积方程理论中勒贝格积分与黎曼积分的结合
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010057
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 and applied.

摘要 以标量和矢量维纳-霍普夫方程为例，我们考虑了在研究和求解积分卷积方程问题中结合黎曼积分和勒贝格函数空间选项的两种方法。我们使用了非线性因式分解方程法和核平均法。引入并应用了直接黎曼可积分性的广义。
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引用次数: 0
A characterization of Gibbs semigroups 吉布斯半群的表征
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010069
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.

摘要 我们提出了吉布斯半群的一个新特征，它是对紧凑半群类似特征的扩展。
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引用次数: 0
Ternary $$Z_3$$ -symmetric algebra and generalized quantum oscillators 三元 $$Z_3$$ - 对称代数和广义量子振荡器
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010070
R. Kerner

Abstract

We present a generalized version of a quantum oscillator described by means of a ternary Heisenberg algebra. The model leads to a sixth-order Hamiltonian whose energy levels can be discretized using the Bohr–Sommerfeld quantization procedure. We note the similarity with the (Z_3)-extended version of Dirac’s equation applied to quark color dynamics, which also leads to sixth-order field equations. The paper also contains a comprehensive guide to (Z_3)-graded structures, including ternary algebras, which form a mathematical basis for the proposed generalization. The symmetry properties of the model are also discussed.

摘要 我们提出了一个用三元海森堡代数描述的量子振荡器的广义版本。该模型引出了一个六阶哈密顿，其能级可以用玻尔-索默费尔德量子化程序离散化。我们注意到它与应用于夸克颜色动力学的狄拉克方程的（Z_3）扩展版本有相似之处，后者也会导致六阶场方程。论文还包含了对(Z_3)级结构（包括三元代数）的全面指导，这构成了所建议的泛化的数学基础。论文还讨论了模型的对称性。
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引用次数: 0
On Dirichlet problem 关于 Dirichlet 问题
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010045
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 dedicate to the century of V. S. Vladimirov birthday. Its main content is the review of the results in that direction, including the proves of new statements and discussion of unsolved problems. Our goal is to convince readers that, in this “principal” problem of mathematical physics, we know far from everything even about the case of linear equation. There are many interesting and important unsolved problems in that direction.

摘要 在高斯提出拉普拉斯方程的狄利克特问题后的近两个世纪里，许多著名数学家都致力于这一课题及其各种推广研究。他们获得了许多有趣而重要的结果，这些结果已经成为经典。我们的论文是作者在弗拉基米洛夫（V. S. Vladimirov）百年诞辰国际会议上发言的扩展。论文的主要内容是对该领域成果的回顾，包括新声明的证明和未决问题的讨论。我们的目标是让读者相信，在这个数学物理的 "主要 "问题上，即使是线性方程的情况，我们知道的也远远不够。在这个方向上还有许多有趣而重要的未决问题。
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引用次数: 0
Recent progress in the theory of functions of several complex variables and complex geometry 若干复变函数和复几何学理论的最新进展
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010112
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 submodule sheaves associated to singular Nakano semipositive Hermitian metrics on holomorphic vector bundles.

摘要 我们对（L^2）理论的两个主要部分--（L^2）存在定理和（L^2）扩展定理--的会话的最新进展，以及它们在获得格里菲斯实在性标准和全形向量束（奇异）赫米特度量的中野实在性特征方面的应用进行了综述、以及与全形向量束上奇异中野半正赫米提度量相关的乘子子模剪的强开放性性质和稳定性性质。
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引用次数: 0
Multidimensional Zaremba problem for the $$p(,cdot,)$$ -Laplace equation. A Boyarsky–Meyers estimate $$p(,cdot,)$$ - 拉普拉斯方程的多维扎伦巴问题。博雅斯基-梅耶斯估计
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s004057792401001x
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.

Abstract We prove the higher integrability of solutions of 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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引用次数: 0
Some new methods for studying boundary value problems for general partial differential equations 研究一般偏微分方程边界值问题的一些新方法
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010033
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.

摘要 我们考虑了研究域中线性偏微分方程边界值问题的方法，而不管方程的类型如何。我们提出了几种研究边界值问题的方法，这些方法通常基于格林公式。我们以前的出版物专门讨论了这些方法，本文将以总结的形式介绍这些成果。
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引用次数: 0
Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems 弗拉索夫-麦克斯韦-爱因斯坦型方程及其后果。天体物理问题的应用
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924020041

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 the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class.

摘要 我们考虑了一种利用广义相对论爱因斯坦-希尔伯特作用获得相互作用大质量带电粒子系统哈密顿动力学方程的方法。在广义相对论情况下，推导出了非相对论和弱相对论极限下的弗拉索夫型方程。还提出了对泊松方程修正的表达式，这些修正可能有助于暗物质和暗能量的有效作用。在这种情况下，提出了同步多粒子系统中不同粒子适当时间的有效方法。根据得到的作用表达式，我们分析了爱因斯坦方程中宇宙学项的复合结构的可能性。利用流体力学替代法推导出了导致米尔恩-麦克雷宇宙学模型的还原欧拉方程，并在自相似类中求解了该方程。
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引用次数: 0
Geometry and quasiclassical quantization of magnetic monopoles 磁单极子的几何与准经典量子化
IF 1 4区 物理与天体物理 Q3 Mathematics
Theoretical and Mathematical Physics
Pub Date : 2024-02-01 DOI: 10.1134/s0040577924010094
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.

摘要 我们介绍了导致产生磁荷概念的基本物理和数学思想（居里夫人、达尔布、庞加莱、狄拉克），黎曼流形上磁单极子的磁拉普拉斯的一般构造，以及科久科夫和作者关于这些算子的等差数列的准经典近似的结果。
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引用次数: 0
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