  A family of exact sum rules for the one-polaron spectral function in the
low-density limit is derived. An algorithm to calculate energy moments of
arbitrary order of the spectral function is presented. Explicit expressions are
given for the first two moments of a model with general electron-phonon
interaction, and for the first four moments of the Holstein polaron. The sum
rules are linked to experiments on momentum-resolved photoemission
spectroscopy. The bare electronic dispersion and the electron-phonon coupling
constant can be extracted from the first and second moments of spectrum. The
sum rules could serve as constraints in analytical and numerical studies of
electron-phonon models.

Strongly Correlated Electrons