Resolution of Gaussʹ law in Yang-Mills theory by gauge-invariant projection: Topology and magnetic monopoles Original Research Article

An efficient way of resolving Gaussʹ law in Yang-Mills theory is presented by starting from the projected gauge-invariant partition function and integrating out one spatial field variable. In this way one obtains immediately the description in terms of unconstrained gauge-invariant variables which was previously obtained by explicitly resolving Gaussʹ law in a modified axial gauge. In this gauge, which is a variant of ʹt Hooftʹs Abelian gauges, magnetic monopoles occur. It is shown how the Pontryagin index of the gauge field is related to the magnetic charges. It turns out that the magnetic monopoles are sufficient to account for the non-trivial topological structure of the theory.