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Invariants of magnetic lines for Yang-Mills solutions

Journal of Geometry and Physics. 2024. Vol. 198. Article 105102.
P. M. Akhmet'ev, Dvornikov M. S.

We construct a new Yang-Mills 3D-solution on the space of negative scalar curvature. 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
coincides with a physical Kolmogorov scale. This gives an estimation of α-effect by the
dispersion of the asymptotic ergodic Hopf invariant in the asymptotic limit with a negative
scalar curvature parameter.
 

Research target: Physics Mathematics
Language: English
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Keywords: properties of geodesic flowsуравнения Янга-Миллсаmagnetic helicity
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