On confinement in a light-cone Hamiltonian for QCD

TL;DR

This paper develops a non-perturbative, symmetry-preserving Hamiltonian approach for QCD in light-cone gauge, enabling the retrieval of many-body gauge field effects from a simplified quark-antiquark framework, with potential implications for confinement.

Contribution

It introduces a novel non-perturbative method using iterated resolvents and discretized light-cone quantization to analyze QCD without traditional truncations, maintaining all symmetries.

Findings

Higher Fock-space amplitudes can be self-consistently derived from quark-antiquark solutions.

The approach respects all Lagrangian symmetries, including covariance and gauge invariance.

The method suggests a mechanism for confinement through the interplay of the QCD scale and additional mass scales.

Abstract

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the $q\bar q$-space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement.