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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 [5, Chap. 3], see also the book by Mahan [8]). More recently, it has been applied also to quantum-electrodynamics by Shabaev et al. [11]. As a background, we shall first consider the classical Green’s function.

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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 [7], while that of Fetter and Walecka [5] differs by a factor of 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 (5.3.1) and (5.3.1), 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.

References

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Authors and Affiliations

  1. Department of Physics, University of Gothenburg, Aschebergsgatan 17, SE-412 96, Göteborg, Sweden

    Ingvar Lindgren

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  1. Ingvar Lindgren
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Lindgren, I. (2011). Green’s Functions. In: Relativistic Many-Body Theory. Springer Series on Atomic, Optical, and Plasma Physics, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8309-1_5

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  • DOI: https://doi.org/10.1007/978-1-4419-8309-1_5

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