The background field method for measuring the electric polarizability of the neutron is adapted to the dynamical quark case, resulting in the calculation of (certain space-time integrals over) three- and four-point functions. Particular care is taken to disentangle polarizability effects from the effects of subjecting the neutron to a constant background gauge field; such a field is not a pure gauge on a finite lattice and engenders a mass shift of its own. At a pion mass of m_pi = 759 MeV, a small, slightly negative electric polarizability is found for the neutron.
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