ar X iv : h ep - p h / 05 08 23 2 v 1 2 2 A ug 2 00 5 High Energy Evolution - The Wave Function Point of View ∗

These lectures deal with the description of hadronic scattering at high energies, and more specifically with the evolution of the scattering matrix with energy[1],[2]. It has been a very lively and active field for the last 10 years[3],[4],[5],[6] and especially lately there has been a new burst of activity. The latest developments are related to what is sometimes called Pomeron loops[7], or Fluctuations[8] or alternatively Saturation effects in the projectile wave function[4]. It is the last characterization that is most suited to the nature of these lectures. Somehow, although the physical underpinning of the low x (or high energy) evolution is the understanding how hadronic wave functions evolve with energy, the language of the wave function is not frequently used in this context. I believe that one can learn a lot by dealing directly with the wave function, since it contains all the nontrivial information there is to have, so my heart goes out to the wave function. I have therefore decided for these lectures to adhere to its point of view on Life, the Universe and Everything, and as a small part of Everything, to show how to think about the evolution and derive the evolution equation from this perspective. The high energy evolution in its latest incarnation became more or less synonymous with saturation. Why is it interesting to study high energy evolution? One obvious answer is of course that there is an experimental