  Following earlier work on the same topic, we consider once more scalar field
theories on the world sheet parametrized by the light cone coordinates. For
most of the way, we use the same approach as in the previous work, but there is
an important new development. To avoid the light cone singularity at p^{+}=0,
one world sheet coordinate had to be discretized, introducing a cutoff into the
model.In the earlier work, this cutoff could not be removed, making the model
unreliable. In the present article, we show that, by a careful choice of the
mass counter term, both the infrared singularity at p^{+}=0 and the ultraviolet
mass divergences can be simultaneously eliminated. We therefore finally have a
cutoff independent model on a continuously parametrized world sheet. We study
this model in the mean field approximation, and as before, we find solitonic
solutions. Quantizing the solitonic collective coordinates gives rise to a
string like model. However, in contrast to the standard string model, the
trajectories here are not in general linear but curved.

High Energy Physics - Theory