Classical Gluon Fields and Small X Physics

I present a recent review of work which attempts to describe the small x part of a hadron wavefunction in terms of classical gluon elds. I try to motivate this approach, describe the class of problems which might be solved, and the current status of the method. In this talk and a later one by Pivovarevv1] at this meeting, you will hear of attempts to describe the small x part of the hadron wavefunction by classical elds. It is worthwhile therefore to have an intuitive understanding of why such an approach may be useful. The physics of small x is that of a high density of gluons. If we take the gluon density scaled by the cross section of the hadron of interest, = R 2 , we can deene a dimensionful quantity 2 = dN=dy==R 2 (1) Here dN=dy is the multiplicity of gluons per unit rapidity, and the rapidity is dy = dx=x where x is Bjorken x. (We shall describe these kinematic variables more later in this talk.) The data from HERA indicate that dN=dy is increasing rapidly as x ! 0, so that at arbitrarily large x, we have QCD (2) This suggests, and we shall make the arguments stronger in this talk, that the theory is described by weakly coupled QCD