Full-zone fermionic Nambu energy counting ($H=J{\sum }_k{\Psi }_k^{†}{h}_k{\Psi }_k={\sum }_{k}2J{d}_k({\gamma }_k^{†}{\gamma }_k-1/2)$)

If the traceless matrix $h_k$ has eigenvalues $\pm d_k$ and the Nambu spinor includes an opposite-momentum creation operator, a full-zone sum contains both partners. Its physical quasiparticle energy is $2J{d}_k$, not $J{d}_k$. The negative term becomes a vacuum constant only after normal ordering. In the Ising-chain Nambu spinor, $d_k=\sqrt{1+g^2-2g\cos k}$. A half-zone calculation instead groups one complete two-mode block; changing the momentum range without changing the normalization is inconsistent.