FC210 Advanced QFT

Lectures: Tuesdays 14:00-17:00.
Lectures take place in Prof. Michal Lenc's office "03028", 3rd floor, building 6.

Course Plan, Spring 2024:

Tuesday 20.02.24
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 27.02.24
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. 3. Expand 1PI-effective 3-vertex in its connected constituents. (video)

Tuesday 05.03.24
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 [S] 14. Self-energy at one-loop [S] 14. Wick rotation [S] 14. (video)

Tuesday 12.03.24
Dimensional analysis of phi-cubed theory [S] 12. Mass dimension of amputated diagram. Superficial degree of UV divergence. Integrals via Feynman trick [S] 14. Gamma function [S] 14. Self-energy at one-loop [S] 14.
Hw: 1. Calculate mass dimension of coupling constant of phi-4 theory in d spacetime dimensions. (video)

Tuesday 19.03.24
Vertex Correction [S] 16. On-shell renormalization scheme, Modified Minimal Subtraction (MS-bar) renormalization scheme. [S] 27. Renormalization group, Callan-Symanzik eq. [S] 28. (video)

Tuesday 26.03.24
Dirac spinor, Clifford algebra, Dirac action. Dirac Propagator [S] 43. Berezin integration. Real & complex Grassmann-odd Gaussian integrals [S] 44. (video)

Tuesday 02.04.24
Global Abelian symmetry of correlation functions. Feynman rules & diagrams for fermions [S] 45. One-loop functional determinant [S] 53. (video)

Tuesday 09.04.24
Non-abelian gauge symmetry [S] 69.
Lie algebras and their representation theory. Non-abelian covariant derivative & field strength. Finite & infinitesimal gauge transformations. Yang-Mills (YM) action + matter action [S] 69. Yang-Mills path integral. Gauge-fixing. Faddeev-Popov (FP) ghosts & determinant. Extended Yang-Mills action [S] 71. (video)

Tuesday 16.04.24
Yang-Mills path integral. Gauge-fixing. Faddeev-Popov (FP) ghosts & determinant. Extended Yang-Mills action [S] 71. BRST transformations for Yang-Mills theory [S] 74. BRST cohomology for Yang-Mills theory [S] 74.
Hw: Show that the BRST transformation of the FP ghost is nilpotent. (video)

Tuesday 23.04.24
Propagators & Feynman rules for pure Yang-Mills theory [S] 72. Beta function in pure Yang-Mills theory [S] 73.
Hw: Calculate the contribution to the gluon self-energy from the pure gluon 1-loop diagram with 2 cubic gluon vertices. (video)

Tuesday 30.04.24
Beta function in pure Yang-Mills theory [S] 73. (video)

Tuesday 07.05.24
Beta function in Yang-Mills theory with fermionic matter [S] 73.
Ward identities in QED [S] 67, 68. (video)

Tuesday 14.05.24
Background field method [S] 78, [1001] 6.5.a. Batalin-Vilkovisky (BV) field-antifield formalism. Antibracket. Odd Laplacian. Quantum master equation. Independence of gauge-fixing. Generalized Ward identities. Zinn-Justin equation. (video)

Tuesday 21.05.24
Diagrammatic approach to representation theory [C] 2.2. (video) Exam problems + Feynman Checkerboard. (video)

Tuesday 28.05.24
No lecture.

Exam problems (Latest version: 17.05.24.)

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.