Towards a solution of pure Yang - Mills theory in 3 + 1 dimensions

We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schrödinger representation and the large N , planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important parallel shows up in the analysis of the ground state wave-functional especially in view of the numerical similarity of the existing large N lattice simulations of the spectra of 2+1 and 3+1 Yang Mills theories. [email protected] [email protected] [email protected]