  In this work we discuss an analytic approach towards the solution of pure
Yang-Mills theory in 3+1 dimensional spacetime which strongly suggests that the
recent strategy already applied to pure Yang-Mills theory in 2+1 can be
extended to 3+1 dimensions. We show that the local gauge invariant variables
introduced by Bars gives a natural generalisation to any dimension of the
formalism of Karabali and Nair which recently led to a new understanding of the
physics of QCD in dimension 2+1. After discussing the kinematics of these
variables, we compute the jacobian between the Yang-Mills and Bars variables
and propose a regularization procedure which preserves a generalisation of
holomorphic invariance. We discuss the construction of the QCD hamiltonian
properly regularized and compute the behavior of the vacuum wave functional
both at weak and strong coupling. We argue that this formalism allows the
developpement of a strong coupling expansion in the continuum by computing the
first local eigenstate of the kinetic part of Yang-Mills hamiltonian.
