出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We give a definition of gauge-invariant magnetic monopoles in Yang-Mills theory without using
the Abelian projection due to ’t Hooft. They automatically appear from the Wilson loop operator.
This is shown by rewriting the Wilson loop operator using a non-Abelian Stokes theorem. The
magnetic monopole defined in this way is a topological object of co-dimension 3, i.e., a loop in
four-dimensions. We show that such magnetic loops indeed exist in four-dimensional Yang-Mills
theory. In fact, we give an analytical solution representing circular magnetic monopole loops
joining a pair of merons in the four-dimensional Euclidean SU(2) Yang-Mills theory. This is
achieved by solving the differential equation for the adjoint color (magnetic monopole) field in
the two–meron background field within the recently developed reformulation of the Yang-Mills
theory. Our analytical solution corresponds to the numerical solution found by Montero and
Negele on a lattice. This result strongly suggests that a meron pair is the most relevant quark
confiner in the original Yang-Mills theory, as Callan, Dashen and Gross suggested long ago.
