Hamiltonian YM 2+1: note on point splitting regularization

TL;DR

This paper investigates the Hamiltonian formulation of 2+1 dimensional Yang-Mills theory, focusing on point splitting regularization and exploring how including higher-order regularization terms affects the ground state in the large N limit.

Contribution

It provides a detailed analysis of point splitting regularization in Hamiltonian YM theory and explores the inclusion of positive powers of the regularization parameter to better understand the ground state.

Findings

Inclusion of up to two positive powers of the regularization parameter is feasible.

The approach offers insights into the structure of the vacuum wave functional.

The study advances the understanding of regularization effects in YM Hamiltonian formulations.

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.