Lectures take place in Prof. Michal Lenc's office "03028", 3rd floor, building 6.

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.

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.

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.

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.

Vertex Correction [S] 16. 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. Berezin integration. Real & complex Grassmann-odd Gaussian integrals [S] 44.

Feynman rules & diagrams for fermions [S] 45. One-loop functional determinant [S] 53. 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 & 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.

BRST cohomology for Yang-Mills theory [S] 74. 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.

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

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

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.

Exam problems.

Vanoce.

[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.