HAMILTONIAN-FORMULATION OF 2-DIMENSIONAL GAUGE-THEORIES ON THE LIGHT-CONE

Two-dimensional quantum electrodynamics (QED2) and quantum chromodynamics (QCD2) are studied in the framework of canonical quantization on the light cone. The crucial feature of the present approach is the formulation on a finite interval. This allows resolution of the severe infrared ambiguities of two-dimensional gauge theories and clarification of the relationship between light-cone and equal-time quantization. In particular, the naive lightcone approach emerges as an effective theory with well-defined limitations. For QED2, it is demonstrated that the known non-perturbative phenomena can be obtained on the light-cone. For QCD2, using the light-cone Coulomb gauge, the role of the gauge degrees of freedom for regularizing the infrared singularity of the gluon propagator is exhibited. The structure of the Hilbert space, the properties of the vacuum and of the elementary excitations are addressed. In the chiral limit (vanishing quark mass), analytical result for both SU(N) and U(N) QCD2 are presented. Relativistic many-body techniques are employed to solve the theory in the large N limit, and the quark condensate is evaluated on the light-cone. It is pointed out that the finite interval techniques allow taking advantage of the technical simplification usually attributed to light-cone quantization, even when using ordinary coordinates. This surprising result is intimately connected to Lorentz invariance. © 1991.