rigorous mechanism by which the dynamics of particle is described in the language of a
string. By using the same language, comparison between the actual dynamics of theories is
possible. We shall see, in the case of Gauge theory, that dramatic simplification occurs and
that the world sheet locality is truly a strong condition.
The formal continuum limit of expression (2-5) for the propagator is
Tee Dq DbDce-so (2-6)
where
N M-1 j
DqDbDc <- Hdq'
j= 1 i= 1
So = dr da blc' (q )2 <-- S
The expression (2-6) is precisely the infinite tension limit of the bosonic Lightcone string.
Let us pause and summarize this Lightcone World Sheet picture of a propagator in
free scalar field theory. Figure (2-1) shows how easily this description lends itself to a
graphical representation: We have a world sheet with length T = Na and width p+ = Mm
organized as a lattice. On each site (i,j) E [1, M] x [1, N] lives a momentum variable q'
and a pair of ghost fields bi, c(. The discretization serves as a regulator of the theory.
We continue now to explain the scalar field theory but in less detail and refer the
interested reader to the original paper. In the Lightcone World Sheet interpretation, cubic
vertices of the field theory are places where the world sheet splits into two world sheets.
This is implemented by drawing solid lines on the grid where boundary conditions for b, c
and q are supplied as for the original world sheet boundaries. Vertex factors that must
be present according to the Feynman rules should somehow be inserted at beginnings and
ends of solid lines. It turns out that this can be done by locally altering the action. For