After successful completion of the course, students are able to understand the contents as outlined in detail in the "subject of course" description and to discuss them in written as well as in oral form. Moreover the students will be able to apply the basic concepts of this course to pertinent examples.

Path-integral formulation of quantum field theory (notions of Grassmann variables, generating functionals and effective actions, Gaussian integration, Hubbard-Stratonovich transformation, loop expansion, resummation theory), Wilson's renormalization group (notions of blocks of spin and coarse graining with application the Ising model), functional renormalization group (Wetterich equation, vertex expansion, derivative expansion, multiloop functional renormalization group, Parquet formalism, DMF2RG, density-functional-theory-fRG).

Lecture with strong and active students participation, accompanied by tutorials where relevant problems are independently solved and presented on the board.

Attendance required!

Certificate

Lecture notes will be available.
Additional references for further reading:
- A. Zee. Quantum Field Theory in a Nutshell. Princeton University Press, Princeton, New Jersey, 2nd edition, 2010.
- J.W. Negele and H. Orland. Quantum Many-Particle Systems. Westview Press, Bolder, 1998.
- P. Kopietz, L. Bartosch, and F. Schütz. Introduction to the Functional Renormalization Group. Springer-Verlag, Berlin Heidelberg, 2010. - A. Schwenk and J. Polonyi, editors. Renormalization Group and Effective Field Theory Approaches to Many-Body Systems. Springer-Verlag, Berlin Heidelberg, 2012. - N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J.M. Pawlowski, M. Tissier, and N. Wschebor. The nonperturbative functional renormalization group and its applications. Physics Reports, 0370-1573, 2021. 

Knowledge from the introductory course VU Quantum Theory I as well as VU Statstical Physics I is expected. The attendance of QT2 and/or QFT is recommended.