Vacuum Energies and Effective Potential in Light-Cone Field Theories

Vacuum energies are computed in light-cone field theories to obtain effectivepotentials which determine vacuum condensate. Quantization surfacesinterpolating between the light-like surface and the usual spatial one areuseful to define the vacuum energies unambiguously. The Gross-Neveu, SU(N)Thirring, and O(N) vector models are worked out in the large $N$ limit. Thevacuum energies are found to be independent of the interpolating angle todefine the quantization surface. Renormalization of effective potential isexplicitly performed. As an example of the case with nonconstant orderparameter, two-dimensional QCD is also studied. Vacuum energies are explicitlyobtained in the large $N$ limit which give the gap equation as the stationarypoint.Comment: LaTeX file, 19 page, 1 eps figure, some references adde