Wave function derivation of the JIMWLK equation

We carefully rederive JIMWLK equation using lightcone perturbation theory. Rigorous treatment requires knowledge of the boosted wave function with second order accuracy. We show that in the second order calculation there are several omitted subtleties. The JIMWLK evolution equation is the important part of high energy QCD. Originally, equation was derived using path integral language [1, 2, 3] (see also [4] for generalization). Clear interpretation of equation in terms of parton wave function and its evolution was proposed in [5]. Essential advantage of the wave function derivation is the explicit separation between scattering and evolution. This means that the projectile evolution can be treated irrespective to target. Evolution and scattering are distinct and separated parts of the theory. Scattering is Wilson lines and evolution is a Hamiltonian-driven task. Then, in order to calculate amplitude of realistic process, it is necessary to calculate quasiclassical gauge field generated by projectile and target. In this paper we improve wave function derivation by rigorous treatment of the nonrelativistic perturbation theory applied to lightcone QCD. We take lightcone coordinates where coordinate x+ play role of time in the canonical quantization scheme. In order to make all constraints second class we impose the following common gauge fixing conditions: A+ = 0 ∂μA μ = ∂−A − + ∂iA i = 0 (1) So gauge field A has only two independent degrees of freedom and after quantization we have Aa(~x, x ) = ∫