= Complex Proca Hamiltonian
{title2=$\mathcal H_{\rm red}=|\pi|^2+|\nabla\cdot\pi|^2/M^2+|G_{ij}|^2/2+M^2|\mathbf B|^2$}
For <Minkowski metric> $(+---)$ and $\mathcal L=-G_{\mu\nu}^*G^{\mu\nu}/2+M^2B_\mu^*B^\mu$, use coordinates $B^\mu,B^{*\mu}$. The spatial <canonical momenta> are $\pi_i=G^{*0i}$, $\pi_i^*=G^{0i}$; the temporal momenta vanish. Constraint preservation gives $\partial_i\pi_i=M^2B_0^*$. Eliminating $B_0$ and its conjugate gives the positive reduced <Hamiltonian density> displayed above, up to a spatial surface term. In particular the massive <Gauss law> has a mass-dependent right-hand side; setting it to zero removes a physical longitudinal <particle polarization>.
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