Scalar $QCD_{4}$ on the null-plane

TL;DR

This paper analyzes the Hamiltonian structure of free Yang-Mills and scalar chromodynamics on the null-plane, deriving their constraint structures and Dirac brackets, aligning with known commutators in the literature.

Contribution

It provides a detailed constraint analysis and Dirac brackets for null-plane scalar QCD, extending the understanding of its Hamiltonian formulation.

Findings

Derived the constraint structure for free Yang-Mills and scalar QCD.

Obtained Dirac brackets consistent with known commutators.

Clarified the Hamiltonian dynamics on the null-plane.

Abstract

We have studied the null-plane hamiltonian structure of the free Yang-Mills fields and the scalar chromodynamics ($SQCD_{4}$). Following the Dirac's procedure for constrained systems we have performed a detailed analysis of the constraint structure of both models and we give the generalized Dirac brackets for the physical variables. In the free Yang-Mills case, using the correspondence principle in the Dirac's brackets we obtain the same commutators present in the literature.