By N. N. Bogoliubov
Publication by way of Bogoliubov, N.
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Extra info for Lectures on Quantum Statistics, Vol. 2: Quasi-Averages
6) will be introduced through differentiating Green's functions of the type under consideration. 6), there will be present an additional "inhomogeneous member", We will obtain these averages from averages of products containing no more than s + m - z simultaneous field functions q;. These averages can again be expressed through Green's Functions (of lower order) with the help of spectral representations. 54 LECTURES ON QUANTUM STATISTICS For their calculation it will be convenient to use a momentum energy representation.
Such an approach to the construction of perturbation theory can be generalized for the investigation of degenerate states. In order that the anomalous (partially summed) Green's Functions appear immediately in the zeroth approximation, we add to H 0 terms L1, of the same type as the infinitesimally small additional terms in Hv. " Let us write H~ = Ho + L1; H~ = H 1 - L1 Then, proceeding from the modified decomposition H = H~ +Hf one can construct in the usual way degenerate perturbation theory using an * We speak of the real solution, keeping in mind that the equations can always have a trivial solution which does not satisfy the necessary physical restrictions (for example it may have the wrong spectral structure).
37). 12). Note that in this case w 1 (w, q) = 0, and the pair states
Lectures on Quantum Statistics, Vol. 2: Quasi-Averages by N. N. Bogoliubov