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A family of exact sum rules for the one-polaron spectral function in thelow-density limit is derived. An algorithm to calculate energy moments ofarbitrary order of the spectral function is presented. Explicit expressions aregiven for the first two moments of a model with general electron-phononinteraction, and for the first four moments of the Holstein polaron. The sumrules are linked to experiments on momentum-resolved photoemissionspectroscopy. The bare electronic dispersion and the electron-phonon couplingconstant can be extracted from the first and second moments of spectrum. Thesum rules could serve as constraints in analytical and numerical studies ofelectron-phonon models.Comment: 4 page

Photoemission spectroscopy and sum rules in dilute electron-phonon systems