Hamiltonian YM 2+1: note on point splitting regularization

Abstract

The Hamiltonian of 2+1 dimensional Yang Mills theory was derived by Karabali, Kim and Nair by using point splitting regularization. But in calculating e.g. the vacuum wave functional this scheme was left in favour of arguments. Here we follow up a conjecture of Leigh, Minic and Yelnikov of how this gap might be filled by including all positive powers of the regularization parameter ($\ep \to +0$). Admittedly, though we concentrate on the ground state in the large $N$ limit, only two such powers could be included due to the increasing complexity of the task.