  We show how to compute electromagnetic polarizabilities of charged hadrons
using four-point functions in lattice QCD. The low-energy behavior of Compton
scattering amplitude is matched to matrix elements of current-current
correlation functions on the lattice. Working in momentum space, formulas for
electric polarizability ($\alpha_E$) and magnetic polarizability ($\beta_M$)
are derived for both charged pion and proton. Lattice four-point correlation
functions are constructed from quark and gluon fields to be used in Monte-Carlo
simulations. The content of the functions is assessed in detail and specific
prescriptions are given to isolate the polarizabilities. The connected
quark-line diagrams can be done today as a small lattice project. The
disconnected diagrams are more challenging but are within reach of dedicated
resources for medium to large lattice projects. We also draw attention to the
potential of four-point functions as a multi-purpose tool for hadron structure.
