The first order ground state wave functional for Yang-Mills

The vacuum wave functional in three dimensions

“…The result is in perfect agreement with the expression obtained by the expected replacements of the four dimensional result obtained in Ref. [2]. The results obtained with this method satisfy the Schroedinger equation by construction but not necessarily the Gauss law, though it can be explicitly shown that it does at O(e).…”

“…This constraint is imposed by the Gauss law, and makes that standard quantum mechanics perturbation theory can not be applied. A procedure to overcome this problem was devised in the case of SU (2), and to O(e) in the weak coupling expansion, in Ref. [2].…”

“…A procedure to overcome this problem was devised in the case of SU (2), and to O(e) in the weak coupling expansion, in Ref. [2]. An alternative procedure has also been considered in Ref.…”

“…Yang-Mills theory or gluodynamics). The method outlined by Hatfield [2] can also be applied to the three dimensional case and a general group SU(N) without major modifications. We do so and obtain the O(e) expression for a general group SU(N) in three dimensions.…”

“…We use two different methods to solve the Schroedinger functional equation.One of them generalizes to O(e 2 ) the method followed by Hatfield at O(e) [2]. The other uses the weak coupling version of the gauge invariant formulation of the Schroedinger equation and the ground state wave functional followed by Karabali, Nair, and Yelnikov [3].…”