  A calculational scheme for obtaining the electric polarizability of the
neutron in lattice QCD with dynamical quarks is developed, using the background
field approach. The scheme differs substantially from methods previously used
in the quenched approximation, the physical reason being that the QCD ensemble
is no longer independent of the external electromagnetic field in the dynamical
quark case. One is led to compute (certain integrals over) four-point
functions. Particular emphasis is also placed on the physical role of constant
external gauge fields on a finite lattice; the presence of these fields
complicates the extraction of polarizabilities, since it gives rise to an
additional shift of the neutron mass unrelated to polarizability effects. The
method is tested on a SU(3) flavor-symmetric ensemble furnished by the MILC
Collaboration, corresponding to a pion mass of m_pi = 759 MeV. Disconnected
diagrams are evaluated using stochastic estimation. A small negative electric
polarizability of alpha =(-2.0 +/- 0.9) 10^(-4) fm^3 is found for the neutron
at this rather large pion mass; this result does not seem implausible in view
of the qualitative behavior of alpha as a function of m_pi suggested by Chiral
Effective Theory.
