Yang-Mills fields and Riemannian geometry Original Research Article

It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gaussʹ law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover further constraints physical states must satisfy. For gauge group SU(2), the underlying geometry is Riemannian and based on the group GL(3). The formalism allows also for the inclusion of static color sources and the extension to gauge groups SU(N > 2), both of which are discussed here.