FC210 Advanced QFT

Lectures: Tuesdays 12:00-15:00.
Lectures take place in Prof. Michal Lenc's office "03028", 3rd floor, building 6.

Course Plan, Fall 2025:

Tuesday 16.09.25 at 12:00
Path integral. Propagator. phi-cubed theory. Fourier transformation. Perturbative expansion. Feynman diagrams. Symmetry factors. [S] 8-9.
Hw: 1. Calculate 4-pt function in free scalar theory [P] 1.8.
2. Check the symmetry factors of the phi^3 Feynman diagrams in the 11 Figures 9.1-9.11 of Srednicki [S] by doing the corresponding functional differentiations of the partition function Z[J].

Tuesday 23.09.25
Connected diagrams. Linked cluster thm via replica trick. DeWitt condensed notation. Perturbative expansion. hbar/loop-expansion [IZ] p. 287-288. WKB/stationary phase approximation. Effective/proper action. Tree & 1-loop contributions to eff. action. Bare/free & full propagators and self-energy [S] 14.
Hw: 1. Rewrite Maxwell action in deWitt condensed notation. 2. Expand 3-pt function in connected and disconnected parts.

Tuesday 30.09.25
The Legendre transform of the classical action is the generator of connected trees. Connected diagrams are trees of 1PI vertices with full propagators. Effective/proper action is the generator of 1PI diagrams [S] 21. Vanishing of Tadpoles [S] 9. Renormalization and counterterms of phi-cubed theory [S] 9. Feynman rules. Fourier transformation. Free & full propagators and self-energy.
Hw: 1. Expand 1PI-effective 3-vertex in its connected constituents.

Tuesday 07.10.25
[S] 14. Self-energy at one-loop [S] 14. Wick rotation [S] 14. Integrals via Feynman trick [S] 14. Gamma function [S] 14. Dimensional analysis of phi-cubed theory [S] 12.
Hw: 1. Calculate mass dimension of coupling constant of phi-4 theory in d spacetime dimensions.

Tuesday 14.10.25
Mass dimension of amputated diagram. Superficial degree of UV divergence. Self-energy at one-loop [S] 14. 3-vertex correction at one-loop [S] 16.

Tuesday 21.10.25
On-shell renormalization scheme, Modified Minimal Subtraction (MS-bar) renormalization scheme. [S] 27. Renormalization group, Callan-Symanzik eq. [S] 28. Dirac spinor, Clifford algebra, Dirac action. Dirac Propagator [S] 43.

Tuesday 28.10.25
Holiday. No lecture.

Tuesday 04.11.25

Tuesday 11.11.25

Tuesday 18.11.25

Tuesday 25.11.25

Tuesday 02.12.25

Tuesday 09.12.25

Tuesday 16.12.25
Last lecture.

Course Material:

[P] Problemsheets.
[S] M. Srednicki, "QFT".
[IZ] C. Itzykson & J-B. Zuber, "QFT".
[1001] S.J. Gates Jr, M.T. Grisaru, M. Rocek & W. Siegel, "Superspace, or One thousand and one lessons in supersymmetry", arXiv:hep-th/0108200.
[C] P. Cvitanovic, Birdtracks.