WebBogomolny equations, which are of lower order than the full Lagrange-Euler equations. Therefore, these models are much easier to solve than a generic model, and provide us … Web1.1 Monopole equation Bogomolny’s equation describes static monopoles in Yang-Mills theory. Given a three dimensional Riemannian manifold Y, let Edenote a rank nHermitian vector bundle E!Y, and let Abe a unitary connection on E, let ˚be a skew Hermitian section of the bundle End(E), the section ˚is called a Higgs eld on E(with trivial coe ...
Hecke modi˙cations of Higgs bundles and the extended …
WebMar 7, 2024 · In the study of solitons in flat space, the ‘Bogomolny’, or ‘self-duality’ equations Bogom , D i Φ = 1 2 ϵ i j k F j k, play two, complementary roles. On the one hand, they provide the absolute minima of the energy, yielding static solutions. But they also allow us to reduce the second-order field equations to first-order ones. WebJun 13, 2024 · Download PDF Abstract: We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator, these monopoles can be interpreted as solutions to the Bogomolny equation with a complex gauge group. Alternatively, these equations can be obtained from dimensional reduction of the … fix bare spots in grass
(PDF) Strong necessary conditions and Cauchy problem
WebApr 10, 2024 · In this equation, a, b and c represent the lengths of the three sides of a right triangle, a triangle with a 90-degree angle between two of its sides. The quantity c is the length of the longest ... WebNov 15, 2024 · Solutions of the Bogomolny Equation on R^3 with Certain Type of Knot Singularity. Weifeng Sun. This paper studies the moduli space of solutions to the Bogomolny equation on R^3 with a certain type of knot singularity. For technical reasons, I have to assume the monodromy along the meridian of the knot lies in (0, 1/8) or in (3/8, … WebAug 26, 2024 · The method of der ivation Bogomolny equations (Bogomolny decomposi- tion), by using the strong necessary conditions, was included and applied in [39], [42], [47], and developed in [2]. can lipo batteries be recycled