Decomposition of meron configuration of SU(2) gauge field

TL;DR

This paper analyzes the structure of SU(2) gauge field merons in Minkowski spacetime, decomposing them into fields revealing monopole-antimonopole features and singularities, advancing understanding of gauge configurations.

Contribution

It provides a novel decomposition of SU(2) meron configurations into isovector, isoscalar, and U(1) fields, highlighting their singularities and monopole-like behavior.

Findings

The isovector field $n$ has two singular points and resembles a monopole-antimonopole pair.

The $C_{}$ field also has singular points, while $ ho$ and $\sigma$ are regular.

The $n$ field reduces to a hedgehog configuration in a special case.

Abstract

For the meron configuration of the SU(2) gauge field in the four dimensional Minkowskii spacetime, the decomposition into an isovector field $\bn$, isoscalar fields $\rho$ and $\sigma$, and a U(1) gauge field $C_{\mu}$ is attained by solving the consistency condition for $\bn$. The resulting $\bn$ turns out to possess two singular points, behave like a monopole-antimonopole pair and reduce to the conventional hedgehog in a special case. The $C_{\mu}$ field also possesses singular points, while $\rho$ and $\sigma$ are regular everywhere.