We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin state
s, is included. In this paper, we add the further approximations of taking only the leading color limit and averaging over spins, as is common in parton shower Monte Carlo event generators. Soft gluon interference effects remain with this approximation. We find that the leading color, spin averaged shower in our formalism is similar to that in other shower formulations. We discuss some of the differences.
In this talk I gave a brief summary of leading order, next-to-leading order and shower calculations. I discussed the main ideas and approximations of the shower algorithms and the related matching schemes. I tried to focus on QCD issues and open ques
tions instead of making a inventory of the existing programs.
