Notes on the Hamiltonian formulation of 3D Yang-Mills theory

TL;DR

This paper develops an algebraic algorithm within the Hamiltonian formalism for 3D Yang-Mills theory, enabling recursive calculation of the ground state wave functional and identifying local counterterms for renormalization.

Contribution

It introduces a new algebraic method to obtain the renormalized Hamiltonian and ground state wave functional in 3D Yang-Mills theory using the Karabali-Nair variable.

Findings

The Gaussian part of the wave functional matches previous results by Leigh et al.

The algorithm allows recursive computation of higher-order corrections.

The method successfully identifies local counterterms for renormalization.

Abstract

Three-dimensional Yang-Mills theory is investigated in the Hamiltonian formalism based on the Karabali-Nair variable. A new algorithm is developed to obtain the renormalized Hamiltonian by identifying local counterterms in Lagrangian with the use of fictitious holomorphic symmetry existing in the framework with the KN variable. Our algorithm is totally algebraic and enables one to calculate the ground state wave functional recursively in gauge potentials. In particular, the Gaussian part thus calculated is shown to coincide with that obtained by Leigh et al. Higher-order corrections to the Gaussian part are also discussed.