ARPES is a very powerful experimental technique to directly measure electronic properties and self-energy effects such as electronic correlations. ARPES technique is an application of Einstein's photoelectric effect, which measures the energy and angle of electrons ejected from a surface shined by photon sources. Energy and momentum conservations tell us how electrons are bound within the crystal.

More specifically, the photo-electron intensity is given by the product of A(k,w) and M_i,f. A(k,w) is a direct manifestation of electron band structure and electronic correlations, which has contributed ARPES to become one of the powerful tools in study of condensed matters.