finite volume.

To see that the relations implied by Eq.  \[or for a specific example, the relation in Eq. \] allow lattice matrix elements to be accessed at continuous momentum transfer, first observe that there are no operator self contractions, thus, the momentum injection occurs in the valence sector alone. To separate the valence and sea sectors, we use the partially quenched Lagrangian $$\cL = \sum_{j,k=1}^6 \ol{Q}{}^{\hskip 0.2em j} \left(
 \Dslash + m_Q \right)_j^{\hskip 0.3em k} Q_k
.\label{eq:pqqcdlag}$$ The six quark fields transform in the fundamental representation of the graded $SU(4|2)$ group and appear in the vector $Q = (u, d, j, l, \mathfrak{u}, \mathfrak{d})^{\text{T}}$ that, in addition to the $u$ and $d$ quarks, has ghost quarks $\mathfrak{u}$ and $\mathfrak{d}$, which cancel the closed valence loops, and two sea quarks $j$ and $l$. In the isospin limit, the quark mass matrix of $SU(4|2)$ reads $m_Q = \diag(m_u, m_u, m_j, m_j, m_u, m_u)$.

In a finite box, the quark fields must satisfy boundary conditions that preserve the single valuedness of the action. Such a choice is afforded by twisted boundary conditions of the form $$Q(x + L \hat{\bm{e}}_r) = \exp \left( i \bm{\theta}^a \cdot \hat{\bm{e}}_r \, \ol T {}^a_C \right) Q(x)  
