Chapter 4

Double-Time Green’s Functions

The proper electron interaction hamiltonian is

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with

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This hamiltonian is correct because it gives the correct expectation values. The average value with respect to a two-electron state is Imagekl\Hint\klImage = (kk\ll) – (kl\lk) exactly as the result (coulomb minus exchange) of calculating the average of 1/|Image1Image2| with respect to a two-electron Slater determinant with the spin orbitals uk and ul in “first-quantization”. The full electronic hamiltonian can be expressed as

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It is common to use an alternative notation for the electron-electron interaction integrals Imagerr|ss = (rs|r s), i.e., with the complex conjugate spin orbitals, belonging to the a operators, ...

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