developed. Such a renormalization is of course necessary for a direct numerical .:.:- iech
since infinities cannot be handled by floating point numbers in a computer. i : program
could still be ,.. )loyed to the two dimensional (d scalar field t.. .. -, since it is finite to
begin with. I : dissertation concludes with appendices that describe the implementation
of the : iuter simulation. T do not contain the i.licit source code, since this would
make for countless but rather explains and describes the .... uter code and its
development and organization. T:. actual source code can be obtained from me via e-mail
should the reader be interested.
1.1 Lightcone Variables and Other Conventions
One starts out with so called r '..' variables which for D dimensional Minkowski
vectors X5P are defined as
xK + ( xD-1)
2
x (1 1)
Stransverse components X k are often denoted by vector bold face type, so that the
Minkowski vector is presented by coordinates. (X+ X-, X). T: Lorenz invariant scalar
product of vectors has the form X PY XI Y" X Y X+Y- X-Y+ in the
Lightcone variables.
When D = 4, a case we find ourselves dealing with from time to time. then it is
sometimes convenient to use polarization defined by
xA (XI + 1x)
Xv (XI iX2). 1-2)
T.. the coordinates are (X+, X-, XA, XV) but we do not use a special index because
this choice of coordinates can be treated in the same fashion as Cartesian ones, so that '/k