Decomposition of meron configuration of SU(2) gauge field

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.

18 pages, 5 figures, Sec.4 rewritten. 5 refs. added