Sine-Gordon model and the smallk+region of light-cone perturbation theory

The nonperturbative ultraviolet divergence of the sine-Gordon model is used to study the ${\mathit{k}}^{+}$=0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the nonperturbative ${\mathrm{\beta }}^2$=8π critical point by a light-cone version of Coleman’s variational method. Vacuum bubbles, which are ${\mathit{k}}^{+}$=0 diagrams in light-cone field theory and are individually finite and nonvanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The ${\mathit{k}}^{+}$=0 region of momentum also contributes to connected Green’s functions; the connected two-point function will not diverge, as it should, at the critical point unless diagrams which contribute only at ${\mathit{k}}^{+}$=0 are properly included. This analysis shows in a simple way how the ${\mathit{k}}^{+}$=0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher-dimensional gauge theories starting at two-loop order in light-cone perturbation theory.