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Many-body Green's function approach to attosecond nonlinear X-ray spectroscopy

Closed expressions are derived for resonant multidimensional X-ray spectroscopy using the quasiparticle nonlinear exciton representation of optical response. This formalism is applied to predict coherent four wave mixing signals which probe single and two core-hole states. Nonlinear X-ray signals are compactly expressed in terms of one- and two- particle Green's functions which can be obtained from the solution of Hedin-like equations at the $GW$ level.