相关论文: Weak Geodesics for the deformed Hermitian-Yang-Mil…

With the help of the Seiberg-Witten map for photons and fermions we define a theta-deformed QED at the classical level. Two possibilities of gauge-fixing are discussed. A possible non-Abelian extension for a pure theta-deformed Yang-Mills…

In this paper, we consider second order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $A_2$-weight. We prove that having a generalized…

The space of Sobolev connections, as it has been introduced for studying the variation of Yang-Mills Lagrangian in the critical dimension $4$, happens not to be weakly sequentially complete in dimension larger than $4$. This is a major…

We study the weak continuity of two interrelated non-linear partial differential equations, the Yang-Mills equations and the Gau{\ss}-Codazzi-Ricci equations, involving $L^p$-integrable connections. Our key finding is that underlying…

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…

This paper will discuss a class of semilinear partial differential equations induced by studying the limiting behaviour of Hermitian Yang-Mills metrics. We will study the radial symmetry of the $C^{2}$ global solution of this equation in…

The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact K\"ahler manifolds that corresponds to the special Lagrangian equation in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen proved…

The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…

While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues,…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of…

A dual weak brace is an algebraic structure $\left(S,\,+,\,\circ\right)$ including skew braces and giving rise to a set-theoretic solution of the Yang-Baxter equation. We show that such a map belongs to a family of set-theoretic solutions,…

In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the…

Applying Cho-Faddeev-Niemi decomposition for SU(2) Yang-Mills field, we obtain the Abelian-Higgs Lagrangian by some approximation. Abelian-Higgs Lagrangian with a spontaneous symmetry breaking potential has vortex solutions known as…

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the…

The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…

We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form equations, and the local boundedness turns out to be sharp in more than two dimensions, answering the `Moser…

Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show…

We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…

In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…