FC210 Advanced QFT

Lectures: Tuesdays 13:00-16:00.
Lectures take place in Prof. Michal Lenc's office "03028", 3rd floor, building 6.

Course Plan, Fall 2019:

Tuesday 17.09.19
Path integral. Propagator. phi-cubed theory. Fourier transformation. Perturbative expansion. Feynman diagrams. Symmetry factors. Connected diagrams. [S] 8-9.
Hw: 1. Calculate 4-pt function in free scalar theory [P] 1.8. 2. Handout about symmetry factors.

Tuesday 24.09.19
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 & full propagators and self-energy.
Hw: 1. Rewrite Maxwell action in deWitt condensed notation. 2. Expand 3-pt function in connected and disconnected parts.

Tuesday 01.10.19
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.
Hw: 1. Expand effective 3-vertex in its connected constituents.

Tuesday 08.10.19
Wick rotation [S] 14. Dimensional analysis of phi-cubed theory [S] 12. 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.

Tuesday 15.10.19
Vertex Correction [S] 16. On-shell renormalization scheme, Modified Minimal Subtraction (MS-bar) renormalization scheme. [S] 27. Renormalization group, Callan-Symanzik eq. [S] 28.

Tuesday 22.10.19
Dirac spinor, Clifford algebra, Dirac action. Dirac Propagator [S] 43. Berezin integration. Real & complex Grassmann-odd Gaussian integrals [S] 44.

Tuesday 29.10.19
Feynman rules & diagrams for fermions [S] 45. One-loop functional determinant [S] 53. Non-abelian gauge symmetry [S] 69.

Tuesday 05.11.19
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 & deteminant. Extended Yang-Mills action [S] 71. BRST transformations for Yang-Mills theory [S] 74.
Hw: Show that the BRST transformation of the FP ghost is nilpotent.

Tuesday 12.11.19
BRST cohomology for Yang-Mills theory [S] 74. Propagators & Feynman rules for pure Yang-Mills theory [S] 72.

Tuesday 19.11.19
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.

Tuesday 26.11.19
Beta function in Yang-Mills theory with fermionic matter [S] 73.

Tuesday 03.12.19
Ward identities in QED [S] 67, 68. Background field method [S] 78, [1001] 6.5.

Tuesday 10.12.19
Ward identities in QED [S] 67, 68. Batalin-Vilkovisky (BV) field-antifield formalism. Antibracket. Odd Laplacian. Quantum master equation. Independence of gauge-fixing. Generalized Ward identities. Zinn-Justin equation.

Tuesday 17.12.19
Exam problems.

Tuesday 24.12.19

Exam problems (Latest version: 18.12.19.)

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.