Symplectic approach to lightcone QCD

TL;DR

This paper introduces a symplectic quantization method for lightcone QCD, emphasizing boundary gauge fields' importance, and extends the JIMWLK equation with second-order corrections, also offering insights into scalar field quantization.

Contribution

It develops a symplectic Faddeev-Jackiw quantization approach for lightcone QCD, highlighting boundary gauge fields and extending high energy evolution equations.

Findings

Boundary gauge fields are essential for consistent quantization.

Derived the second-order correction to the JIMWLK equation.

Provided new insights into lightcone scalar field quantization.

Abstract

We develop a symplectic method of quantization of lightcone QCD. We find that boundary gauge fields are crucial for a consistent and complete quantization. By applying the symplectic Faddeev-Jackiw method, we very carefully remove unphysical degrees of freedom and obtain the true phase space and the complete Hamiltonian. The result is important for the high energy QCD evolution and for a further extension of the JIMWLK equation, for which we find the second-order correction. Finally, we make an important note about a peculiarity of four space-time dimensions. In additional, our method sheds new light on the lightcone quantization of a scalar field.