On Deriving the Effective Interaction from the QCD-Lagrangian

TL;DR

This paper develops a non-perturbative method to derive an effective quark-antiquark Hamiltonian from QCD using discretized light-cone quantization and iterated resolvents, avoiding traditional Fock space truncations.

Contribution

It introduces a novel approach combining iterated resolvents and light-cone quantization to derive effective Hamiltonians directly from the QCD Lagrangian without Fock space truncation.

Findings

Effective Hamiltonian acts only in quark-antiquark Fock space.

Higher Fock-space amplitudes can be self-consistently reconstructed.

Method is free of Tamm-Dancoff truncations, resuming perturbative series to all orders.

Abstract

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. 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 Tamm-Dancoff truncations of the Fock space, rather the perturbative series are consistently resumed to all orders in the coupling constant. Emphasis is put on dealing with the many-body aspects of gauge field theory. Important is that the higher Fock-space amplitudes can be retrieved self-consistently from these solutions. (Proceedings Les Houches 1997)