\langle \cP (\bm{B}_\cP, t) \cO_\mu(t') \ol \cN (\bm{P} + \bm{B}_{\cN},0) \rangle 
,\end{aligned}$$ where $\bm{P} = 2 \pi \bm{n} / L$ is the lattice momentum of the neutron, $\bm{B}_\cN = ( \bm{\th}^u + 2 \bm{\th}^d ) / L$, and $\bm{B}_\cP = ( 2 \bm{\th}^u + \bm{\th}^d ) / L$ are the field momenta of the neutron and proton, respectively. Notice the momentum transfer $\bm{q} = (\bm{\th}^u - \bm{\th}^d - 2 \pi \bm{n}) / L $ can be varied continuously.

Some final points are in order. Firstly, isoscalar quantities (which are notoriously difficult to calculate on the lattice) of course cannot be deduced from these techniques. Next, the results trivially extend to the $SU(3)$ and $SU(6|3)$ flavor groups because they contain the valence $SU(2)_V$ isospin subgroup. There are additional matrix element relations in the limit of an exact valence $SU(3)_V$ symmetry; but because this symmetry is badly broken by the light-quark mass difference, we shall not investigate these relations. Finally, at finite volume, the presence of the $B_\mu$ field in the Lagrangian breaks the $SU(2|2)_V$ symmetry and leads to modification of our results. These modifications can be addressed systematically in chiral perturbation theory ().

Nucleon Isovector Magnetic Moment {#s:example}
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In this 