since the energy of the gluon will become larger than the energy of the mother dipole. Hence, we cannot allow too small dipole sizes. The positive light-cone momentum is essentially equal to the energy, and from now on we will refer to it as energy. Let $p_+$ be the energy of the parent dipole and let the gluon be emitted at a rapidity $y$. Denote by $p_{+g}$ the energy of the gluon. We then have $$p_{+g}\leqslant p_+\Rightarrow p_{\perp g}e^{-y}=\frac{1}{r}e^{-y}\leqslant
p_+, \; \; \textrm{hence}\; r\geqslant \frac{e^{-y}}{p_+}$$

This means that we get a very natural cutoff for small dipoles, given by, $\rho (y)=e^{-y}/p_+$. To make the program right-left symmetric, which means that the theory looks the same independent of which way we evolve, we must also demand $p_-$ conservation, which is described later. These observations are the main motivations for this thesis. We will now describe the Monte Carlo program, including energy conservation, developed to study the deeply inelastic scattering between a photon and a nucleus, and between two onium states.

Recoil Formulas
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Since we demand energy to be conserved, we must also take into account the full recoil effects. A single gluon will, in the dipole model, be a part 