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I use Wick's theorem to decompose expectation values of a string of bosonic creation and annihilation operators evaluated at the vacuum state. This can only be done when the time evolution is driven by a Hamiltonian of the form:

[tex]

H=\sum_{i,j}{\epsilon_{i,j} c^{\dagger}_{i}c_{j}} [/tex]

which follows from the functional field integral in the coherent state basis. Now I am being told, that WT can also be applied when the Hamiltonian contains quadratic terms that don't conserve particle number (c dagger, c dagger and c, c terms). Can anyone confirm this? I am still trying to figure out how that is supposed to lead to a gaussian exponential. I'd appreciate it if anyone can provide links or explain me why this is legitimate.

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# A Expert on Wick's Theorem needed

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