Basic Syllabus
The main topics are
1) Second quantization, Wick's theorem, representation of operators, particle-hole formalism, normal-orderer operators, simple diagram rules. Covered by Lecture notes and Shavitt and Bartlett chapter 3 and 4.
2) Hartree-Fock, derivation in coordinate space and second quantization representation, Hartree-Fock Hamiltonian, Brillouin's and Koopman's theorems, stability of Hartree-Fock solution, Thouless' theorem and interpretation of the Hartree-Fock equations. Raimes chapter 3.
3) Density functional theory: Derive the Kohn-Sham equations and make link with Hartree-Fock equations. Hohenberg-Kohn theorems on existence of unique density. Local density approximation from electron gas. (see files dft.pdf and jones.pdf under the Lectures link)
4) Many-body perturbation theory: a) Time-independent: Brillouin-Wigner and Rayleigh-Schroedinger, derive expression for the energy and the wave operator. Set up diagrammatic representation. Chapters 5-7 in Shavitt and Bartlett. b) Time-dependent perturbation theory within the interaction picture. Adiabatic hypothesis and Goldstone's linked diagram theorem. Derive diagram rules. Raimes chapters 5-7.
5) Coupled-cluster theory. Set up the general expressions for the energy and the amplitudes (chapter 10.1-10.4 in Shavitt and Bartlett) at the level of singles and doubles. Use diagram rules to set up expressions, in particular for the T2 operator. Covered by lecture notes and Shavitt and Bartlett chapters 9 and 10.1-10.4.
The syllabus for this course consists of the lecture notes on the webpage, weekly exercises, one midterm project which is marked and counts 30% and a final oral exam.
The recommended textbook (the lectures are based on this text) is I. Shavitt and R.J. Bartlett. Many-body methods in Chemistry and Physics, Cambrige. See the link
Another textbook is E.K.U. Gross, E. Runge and O. Heinonen, Many-particle theory, see this link
Much of the material is also covered by the textbook of Raimes, see the lecture link. The relevant chapters are 1-3, 5-11.
Additional literature
In addition to the text Shavitt and Bartlett, we recommend the texts of Gross, Runge and Heinonen, as well as the text of Raimes. These two texts are out of print and can be found at the webpage under the lecture link. Other good texts are Fetter and Waleca, Quantum theory of many-particle systems, Blaizot and Ripka's Quantum theory of finite systems and finally Negele and Orland's text on Many-body physics. The lectures follow closely Shavitt and Bartlett, but one can also use Gross, Runge and Heinonen and the text of Raimes.
There is also additional material under the lecture notes link that covers coupled-cluster theory and density functional theory.