and the process continues. This is used in the Dipole Cascade Model, [@13; @14], which is formulated in momentum space.

A large part of this thesis is based on Mueller’s Dipole model [@e2; @e3; @e4; @e5] and we will be using it in our MC program. In Mueller’s model we start with a heavy quark-antiquark pair, an onium state, and consider successive emissions of softer and softer gluons. The main idea here is also based on the observation that, in the large $N_c$ limit and in the leading logarithmic approximation the complete, multi-gluon, wavefunction of an onium state can be regarded as a collection of dipoles. This is so since, as we saw above, each gluon will act like a quark-antiquark pair. Mueller’s approach is formulated in transverse position, $\bold{x}$, instead of transverse momentum, $\bold{k}$. These two variables are naturally connected by a Fourier transform $$\psi_{\alpha \beta}^{(0)}(\bold{x}_1,Y)=\int
\frac{d^2\bold{k}_1}{(2\pi)^2}e^{i\bold{k}_1\cdot\bold{x}_1}\psi_{\alpha
  \beta}^{(0)}(\bold{k}_1,Y)$$ Here $\psi$ is the light-cone wavefunction (the zero on $\psi$ indicating that there are 0 gluons present) and $\alpha$ and $\beta$ are heavy quark and antiquark spinor indices, $\bold{x_0}$ and $\bold{x_1}$ are the transverse coordinates of the quark and the antiquark respectively. Finally, $Y$ is the total rapidity range determined by 