Yang–Mills-Inspired Gauge Theory of Superconducting Magnets: Non-Abelian Order, Flux Quantization, and Vortex Engineering

Superconducting magnets are conventionally described by London, Bardeen–Cooper–Schrieffer, and Ginzburg–Landau theories, which are primarily formulated within the Abelian electromagnetic gauge group U(1). Yang–Mills theory provides a generalized framework for non-Abelian local gauge symmetries, in which gauge fields interact through nonlinear field-strength terms. Although ordinary superconductivity is not directly governed by the fundamental Yang–Mills interactions of particle physics, Yang–Mills mathematics can be used to construct effective theories for multicomponent condensates, multiband superconductors, unconventional pairing states, and non-Abelian vortex systems.This paper develops a Yang–Mills-inspired effective model for superconducting magnets. The central hypothesis is that a multicomponent superconducting order parameter may be represented as a field inan internal space governed by an effective gauge group such as SU(2), U(N), or SU(N) × U(1). The proposed theory contains the conventional electromagnetic field as an Abelian sector and additional internal gauge fields associated with relative phase, band conversion, spin, orbital, or pseudospin degrees of freedom.The model generalizes the Ginzburg–Landau free energy and predicts modified penetration depths, additional coherence lengths, composite vortices, generalized flux quantization, and possible topologicalstabilization of magnetic flux. The theory is presented as an effective phenomenological framework rather than as a claim that ordinary superconductors are fundamental Yang–Mills systems.