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Green’s Functions

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Relativistic Many-Body Theory

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 63))

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Abstract

The Green’s function is an important tool with applications in classical as well as quantum physics (for an introduction, see, particularly the book by Fetter and Walecka, The Quantum Mechanics of Many-Body Systems (1971) [67, Chap.3] and also the book by Mahan, Many-particle Physics (1990) [140]).

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Notes

  1. 1.

    Different definitions of the field-theoretical Green’s function are used in the literature. The definition used here agrees with that of Itzykson and Zuber [92], while that of Fetter and Walecka [67] differs by a factor of \(\mathrm {i}\).

  2. 2.

    In our notations, an orbital line between heavy dots always represents an electron propagator.

  3. 3.

    Generally, a diagram is considered closed if it has no free lines/propagators, like the diagrams in (5.60) and (5.61), while an open diagram has at least one pair of free lines, like those in Fig. 5.3. An operator or a function represented by a closed/open diagram is said to be closed/open.

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Correspondence to Ingvar Lindgren .

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Lindgren, I. (2016). Green’s Functions. In: Relativistic Many-Body Theory. Springer Series on Atomic, Optical, and Plasma Physics, vol 63. Springer, Cham. https://doi.org/10.1007/978-3-319-15386-5_5

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