= Quadratic bosonic Hamiltonian
{title2=$H=a^\dagger A a+\tfrac12(a^TBa+\mathrm{h.c.})$}
A quadratic bosonic Hamiltonian contains terms of degree two in <bosonic creation operators> and <bosonic annihilation operators>, with an optional constant. The number-conserving <matrix> $A$ is <Hermitian> and the pair <matrix> $B$ may be taken <symmetric matrix>[symmetric]. Positive stable forms can be diagonalized by a canonical <Bogoliubov transformation>; the strict stability condition matters at <zero modes>.
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