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Atomic and Condensed Matter
Studying Green's function in many body physics
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[QUOTE="king vitamin, post: 6173398, member: 134222"] It seems that all three of your questions concern what the relation is between the Green's function in many-body physics and physical/experimental observables. One very clear connection is the fact that the spectral function is obtained from the retarded two-point correlation function as $$ \rho(\omega) = \mathrm{Im} G_{\mathrm{R}}(\omega) = \pi \sum_{\alpha} | \langle \alpha | \psi | 0 \rangle|^2 \left[ \delta(\omega - E_{\alpha} + E_0) \mp \delta(\omega + E_{\alpha} - E_0) \right] $$ where the upper (lower) sign is for bosons (fermions). But this form - a matrix element times a delta function constraining energy conservation - is precisely the form of Fermi's Golden Rule which computes the transition rate of time-dependent processes which couple to the operator ##\psi#. In addition, this object is only nonzero at precisely the frequencies where the many-body system has energy levels, so it tells you about the spectrum of your system. These two facts result in a lot of relations between experimental observables and spectral functions. For more details, Piers Coleman's many-body textbook has about half a chapter devoted to relating spectral functions to various experimental observables in different systems. It is far more detailed and clear than anything I could write up here, so I highly recommend checking it out. [/QUOTE]
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Studying Green's function in many body physics
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