Classical field theory, symmetries and conservation laws.
Lorentz invariance, representations, spinors, vectors.
Second quantization, perturbation theory, Feynman diagrams.
Quantization of QED, calculation of some tree level S-matrix elements.
One-loop renormalization of QED.
These two chapters will be covered for sure:
Basics (PS10, W12)
Renormalization and Symmetry (PS11, Aspects 4)
Renormalization group (PS12,W18)
Critical Exponents, epsilon expansion, Wlison-Fisher (PS 13)
-- Gauge Theories (PS 15-16, Weinberg I 12) (maybe: QCD processes PS17, OPEs PS18, W20)
List of potential special topics:
Effective potentials (Weinberg 16).
-- Symmetry Breaking PS20, W19+21 and Aspects 5, Weinberg 19.
-- Quantization of gauge theories (PS 21, Weinberg 15,17)
-- Anomalies: PS19 + Aspects 3, W22.
-- Solitons (Aspects 6) and Instantons (aspects 7), W23.
-- Large N (Aspects 8)
-- 2D field theories, integrability, CFTs, bosonization.
-- Finite T field theories, more generally statistical field theory.
-- Non-equilibrium, SK actions, MSR actions and stochastic processes.
-- Bound state problems, Bethe-Salpeter equations (IZ).
Peskin and Shoreder: An Introduction to Quantum Field Theory.
Coleman: Aspects of Symmetry.
Weinberg: The Quantum Theory of Fields, volumes I and II.
Zinn-Justin: Quantum Field Theory and Critical Phenomena.
Amit: Field Theory, the Renormalization Group and Critical Phenomena.
Itzykson and Zuber: Quantum Field Theory.
Kamenev: Field Theory of Non-Equilibrium Systems