approach -i.-.-, -. 1 a world sheet description which was non-local on the sheet. A similar,
but local, world sheet was much later explicitly constructed by Bardakci and Thorn [5]
and their formalism is essentially the backdrop and foundation to the work presented here.
We will in this dissertation present work that has been done in the framework of
this explicit local world sheet description of well-known field theories. In Chapter 1 we
discuss this setting in general, the planar diagram approach and the light-cone. In Chapter
2 we present in some detail the Lightcone World Sheet established by Bardakci and
Thorn and later developed by them and others. The approach is to maintain clarity and
leave details and technicality in the original work. Next we turn to the two themes of
the dissertation. In Chapter 3 we discuss standard field theoretic perturbation theory in
the Lightcone World Sheet setting; since the world sheet mapping is done diagram per
diagram this should yield entirely known results but now in the context of a different
regulator. This chapter is almost entirely a recap from articles which I coauthored
[6] and [7]. It serves both to familiarize the reader with the setting and to test the
formalism in the perturbative limit. Chapter 4 deals with the formalism in a different
and complementary way, namely by use of numerical methods which are most effective
in the strong coupling regime. It was outside the scope of the current thesis to complete
the numerical investigation for other theories than the simplest ones that the Lightcone
World Sheet formalism had been developed for, namely two dimensional f3 scalar field
theory. We employ Monte Carlo methods similar to those of lattice gauge theory but on
the world sheet system describing the field theory. Although the general methodology of
Monte Carlo simulations has been well established, not only in lattice gauge theory and
statistical physics but in a wide range of applied mathematical settings, the application
here is completely novel and required the development of specialized computer programs.
It was partly for this reason that time did not permit a numerical investigation of more
interesting field theories, but mainly the reason was that at the time when this work was
done, the renormalization procedure for the more complicated theories had not yet been