English

Invariants of magnetic lines for Yang-Mills solutions

Algebraic Topology 2024-01-24 v2

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 α\alpha-effect by the dispersion of the asymptotic ergodic Hopf invariant in the limite with a negative scalar curvature parameter.

Keywords

Cite

@article{arxiv.2312.06301,
  title  = {Invariants of magnetic lines for Yang-Mills solutions},
  author = {Petr Akhmet'ev and Maxim Dvornikov},
  journal= {arXiv preprint arXiv:2312.06301},
  year   = {2024}
}