Introduction to Green functions and many-body perturbation theory

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2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . . . . . . . . 7 2.3.2 Green functions in other bases . . . . . . . . . . . . . . . . . . . . . . 7 2.3.3 k-space Green function in translationally invariant systems . . . . . . 8 2.3.4 Fourier transformed Green functions (in the time-frequency domain) . 8 2.4 Example: Green function for noninteracting electrons . . . . . . . . . . . . . 8 2.5 The Lehmann representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.6 The spectral function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6.1 Sum rule and physical interpretation . . . . . . . . . . . . . . . . . . 12 2.6.2 Spectral function for noninteracting fermions and Fermi liquids . . . 13 2.6.3 Relation to momentum distribution (through weighted sum over ω) and to density of states (through sum over k) . . . . . . . . . . . . . 14

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Introduction to Green functions and many-body perturbation theory

2 The single-particle retarded Green function and its spectral function 4 2.1 Retarded, advanced, “greater”, and “lesser” single-particle Green functions . 4 2.2 The meaning of 〈· · ·〉 and the time dependence . . . . . . . . . . . . . . . . . 5 2.3 Some other forms of the Green functions . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Transformations to other bases . . . . . . . . . . . . . . ....

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تاریخ انتشار 2013