= Full-zone fermionic Nambu energy counting
{title2=$H=J\sum_k\Psi_k^\dagger h_k\Psi_k=\sum_k2Jd_k(\gamma_k^\dagger\gamma_k-1/2)$}
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 $2Jd_k$, not $Jd_k$. 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.
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