Positive-wavevector sum for a real field
= Positive-wavevector sum for a real field
For a real field, $\phi_{-\mathbf q}=\phi_{\mathbf q}^*$. A sum $\sum_{\mathbf q}^{+}$ takes one representative from each nonzero pair $\{\mathbf q,-\mathbf q\}$ so that every independent complex Fourier amplitude is counted once.