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arXiv · 2312.06301

Invariants of magnetic lines for Yang-Mills solutions

Petr Akhmet'ev·Maxim Dvornikov
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Abstract

We construct a new Yang-Mills 3D-solution on the space of negative scalar curvarure. We discuss a problem of non-abelian gauge symmetry is broken with the assumption that a scalar curvature of the domain is a negative small parameter. In this case we use the following fact: a geometrical scale related with Vassiliev's discriminant of magnetic lines coincids with a physical Kolmogorov scale. This gives an estimation of $\alpha$-effect by the dispersion of the asymptotic ergodic Hopf invariant in the limite with a negative scalar curvature parameter.

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Petr Akhmet'ev, Maxim Dvornikov. 2023-12-11. Invariants of magnetic lines for Yang-Mills solutions. https://doi.org/10.1016/j.geomphys.2024.105102

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