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Abstract
The background field method has been used successfully to determine hadron electromagnetic
polarizabilities. Recently questions have been raised regarding the proper way to
deal with the electric field on the lattice. In this paper, we show how the presence
of a background electric field affects the quark hopping matrix. We use this formulation
to carry out simulations on quenched configurations, and we present the results for
neutron electric polarizability for pion masses as low as \(500\MeV\). We find that
the polarizability is roughly constant for the quark masses considered, \(\alpha\sim
1.5 \times 10^{-4} \fm^3\). While the polarizability is positive, it is significantly
smaller than the experimental value due to the fact that the quark masses used are
too large.