Abstract
Basic ideas of quantum many-body theory. Qualitative picture of quasiparticles. Thomas-Fermi screening. Plasmons. Propagators and path integrals in a one-body quantum theory. Aharonov-Bohm effect. Perturbation theory for a propagator. Second quantization and field operators.
When asked to calculate the stability of a dinner table with four legs, a theorist rather quickly produces the results for tables with one leg and with an infinite number of legs. He spends the rest of his life in futile attempts to solve the problem for a table with an arbitrary number of legs.
A popular wisdom.
From the book “Physicists keep joking:”
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Notes
- 1.
The dependence (1.8) is often called the Yukawa potential Yukawa potential, though in the context of screening of the Coulomb potential in (classical) plasma it was derived by DebyeDebye!Huckel screening length@Debye!Hückel screening length and Hückel, with a different screening length, \(\lambda _{\mathrm{D}}\sim \sqrt{k_{B}T}/(ne)\). (The difference is due to the use of the Boltzmann instead of the Fermi distribution in a nondegenerate gas.)
- 2.
It is not so easy to calculate the prefactor \(F_{\odot }\); but it is not difficult to show that it is small only as a power of the parameter \(\lambda _{F}/L\).
- 3.
We will omit the hats over the field operators when it does not create confusion.
- 4.
For the eigenstates of \(\mathcal {N}\), as one should expect, the results are close to the uniform distribution of \(\varphi \) in the interval \([0,\ 2\pi )\).
References
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Zagoskin, A. (2014). Basic Concepts. In: Quantum Theory of Many-Body Systems. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-07049-0_1
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