Abstract
The Green functions is an indispensable tool for studying interacting particles. The usefulness of the Green functions will be shown in the succeeding chapters. Here we give a brief self-contained introduction to the Green functions, their basic properties and applications.
What I cannot create, I do not understand. (R. Feynman)
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Notes
- 1.
Also called Matsubara Green function since they appeared in the seminal paper [11].
- 2.
Here by ρ j μσ μ we mean the operator tensor product ρ j μ ⊗σ μ (for details, see Appendix A.1.5). For brevity, we omit the tensor product notation throughout the book.
- 3.
The thermodynamic “frequencies” are also called Matsubara frequencies.
- 4.
We use the opposite signs for the fermion- and boson-type Green functions, just as in [9].
- 5.
In the fermion-type temperature Green function (6.23) the “time”-ordering operator had the minus sign. Here the “time”-ordering operator gets the plus sign because each \(\varDelta \mathbb{M}_{\alpha }(\mathbf{q},\tau )\) consist of two creation-annihilation operators.
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Melnikov, N.B., Reser, B.I. (2018). Green Functions at Finite Temperatures. In: Dynamic Spin-Fluctuation Theory of Metallic Magnetism. Springer, Cham. https://doi.org/10.1007/978-3-319-92974-3_6
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