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Invariants of magnetic lines for Yang-Mills solutions

Petr Akhmet'ev, Maxim Dvornikov

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

Invariants of magnetic lines for Yang-Mills solutions

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 -effect by the dispersion of the asymptotic ergodic Hopf invariant in the limite with a negative scalar curvature parameter.
Paper Structure (5 sections, 29 equations)

This paper contains 5 sections, 29 equations.

Table of Contents

  1. Introduction
  2. Yang-Mills field and Chern-Simons invariant
  3. Geodesic flows of positive and negative curvature
  4. $M$-invariant of magnetic lines
  5. Discussion