Full-zone antiferromagnetic Nambu counting

For a rotated nearest-neighbour chain, a full-zone sum of $JS(a_k^{†},a_{-k})M_k(a_k,a_{-k}^{†}{)}^T$ contains a normal-ordering constant $JSN$. Rewriting the classical constant as $-JNS(S+1)$ compensates it. One must not additionally halve the sum without changing mode counting.