Quantum Chromodynamics and Other Field Theories on the Light Cone

TL;DR

This work reviews the light-cone (front-form) quantization of gauge theories and its use as both a Hamiltonian framework for nonperturbative QCD bound-state calculations and a practical method for simulating quantum field theories. It develops the light-cone Fock-space formalism, clarifies vacuum structure, and outlines discretized (DLCQ) implementations that render bound-state spectra tractable, including detailed treatment of QED and QCD dynamics in 1+1 and 3+1 dimensions. The text presents perturbative rules in the front form, illustrates with explicit examples (qq̄ scattering, mass renormalization, anomalous magnetic moment), and demonstrates how light-cone wavefunctions encode form factors, structure functions, and exclusive amplitudes. It then surveys the impact on hadronic and nuclear physics, including PQCD factorization, color transparency, and the reduced amplitude formalism, while outlining renormalization and effective interaction strategies essential for extending DLCQ to realistic 3+1-dimensional QCD. The overall message is that light-cone quantization provides a frame-independent, physically intuitive, and computationally viable path to connect QCD’s fundamental degrees of freedom to hadronic observables, albeit with significant technical challenges in nonperturbative renormalization and zero-mode treatment that remain active research areas.

Abstract

We discuss the light-cone quantization of gauge theories as a calculational tool for representing hadrons as QCD bound-states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The light-cone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of light-cone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavy-quark contributions to structure functions. Discretized light-cone quantization, is outlined and applied to several gauge theories. We also discuss the construction of the light-cone Fock basis, the structure of the light-cone vacuum, and outline the renormalization techniques required for solving gauge theories within the Hamiltonian formalism on the light cone.

Figures (36)

• Figure 1: Dirac's three forms of Hamiltonian dynamics.
• Figure 2: The Hamiltonian matrix for a SU(N)-meson. The matrix elements are represented by energy diagrams. Within each block they are all of the same type: either vertex, fork or seagull diagrams. Zero matrices are denoted by a dot ($\cdot$). The single gluon is absent since it cannot be color neutral.
• Figure 3: Calculation of the form factor of a bound state from the convolution of light-cone Fock amplitudes. The result is exact if one sums over all $\Psi_n$.
• Figure 4: (a) Illustration of a vacuum creation graph in time-ordered perturbation theory. A corresponding contribution to the form factor of a bound state is shown in figure (b).
• Figure 5: A few selected matrix elements of the QED front form Hamiltonian $H = P_+$ in KS-convention.