  The many-body theory of photoemission in solids is reviewed with emphasis on
methods based on response theory. The classification of diagrams into loss and
no-loss diagrams is discussed and related to Keldysh path-ordering
book-keeping. Some new results on energy losses in valence-electron
photoemission from free-electron-like metal surfaces are presented. A way to
group diagrams is presented in which spectral intensities acquire a
Golden-Rule-like form which guarantees positiveness. This way of regrouping
should be useful also in other problems involving spectral intensities, such as
the problem of improving the one-electron spectral function away from the
quasiparticle peak.
