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I show that the high energy evolution equations currently in circulation violate S-channel unitarity when viewed as evolution of the target. This violation affects scattering amplitudes when the energy is high enough. I discuss in detail a zero dimensional toy model, where the same problem exists, and show how it can be cured by modifying the evolution Hamiltonian. I then discuss these issues in the framework of JIMWLK evolution and an attempt to extend it using similar ideas.
https://bnl.zoomgov.com/j/1601581422?pwd=dkdxVFgyRTZESUxIbUZDN1RmRURPQT09