In mathematical terms, topological vortices are based on polar coordinate transformations of complex fields, using Euler's formula to express the field as ϕ(x) = r_ϕ(x) e^(iθ_ϕ(x)), where the winding number n in θ_ϕ(x) = nθ_x + φ determines the topological properties of the vortex—when the spatial coordinate angle θ_x rotates by 2π, the field angle rotates n times. This structure appears in the potential energy landscape as a minimum-value ring of the "Mexican hat" potential, corresponding to continuous variations of the ground state in field theory.
Although Derrick's theorem indicates the instability of steady-state topological objects in higher dimensions, the introduction of gauge fields can counteract the energy divergence caused by derivative terms, theoretically stabilizing the vortex configuration.
English
French
Spanish
Portuguese
Deutsch
Turkish
Dutch
Italiano
Russian
Romaian
Portuguese (Brazil)
Greek
简体中文
日本語
한국어
繁体中文