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Many-body Green’s Functions

This article provides solutions for exercises 15-18 related to the calculation of second-order diagrams and evaluation of the single loop bubble in the Green's Function equations of motion. The methods, including obtaining self-energy and closing the contour, are explained in detail.

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Many-body Green’s Functions

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  1. Many-body Green’s Functions • Exercise (15) Solution: 10 second order diagrams for the Green’s function

  2. Equation of Motion for the Green’s Function • Exercise (16) Solution: 10 second order diagrams for the Green’s function • To obtain self energy, cut off Go at either end to leave stubs • There are six proper self-energy diagrams at second order

  3. Evaluation of the Single Loop Bubble • Exercise (17) Solution: Same result by closing the contour in the lower half plane

  4. y x Evaluation of the Single Loop Bubble • Exercise (18) Solution: continued • For

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