= Number-conserving Gaussian quantum state
Here number-conserving means invariant under a global particle-number <quantum phase> rotation: the field mean and anomalous averages $\langle\psi\psi\rangle$ vanish. It does not mean a sharp total particle number. All normal correlations are obtained by Wick pairings of the <one-body density matrix>. Independent thermal bosonic modes satisfy this rule; generic nonvacuum bosonic <number states> do not. A <Slater determinant> is the analogous fermionic pairing state.
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