= Lehmann representation
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A <Lehmann representation> inserts complete <energy> eigenstates into a <correlation function>, expressing its frequency dependence through transitions and operator <matrix elements>. For a Hermitian <bosonic> operator in a thermal retarded <correlation function>, the spectral weights contain $(p_n-p_m)|A_{nm}|^2$ at <energy> differences $E_m-E_n$.
Here $p_n=e^{-\beta E_n}/Z$. A Wightman <correlation function> instead has the appropriate single occupation weight rather than the same difference, and <fermionic> ordering changes the thermal combination. The chosen <correlation function> therefore matters. This representation connects spectral features to allowed transitions and provides the basis for analytic continuation between imaginary- and real-frequency functions. A transition continuum produces a continuous spectral contribution rather than only isolated poles.
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