We show how to compute electromagnetic polarizabilities of charged hadrons without the use of background fields in lattice QCD. The low-energy behavior of the Compton scattering amplitude is matched to matrix elements of current-current correlation functions on the lattice. Working in momentum space, formulas for electric polarizability (𝛼 𝐸 ) and magnetic polarizability (𝛽 𝑀 ) are derived for both charged pion and proton. Lattice four-point correlation functions are constructed from quark and

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... luon fields to be used in Monte-Carlo simulations. We also draw attention to the potential of four-point functions as a multi-purpose tool for hadron structure.