Physics 508 : Quantum Field Theory

Administrative Details:

The course will meet Mondays, Wednesdays and Fridays 2-3 in Hennings 302. We have the room Mondays and Fridays 3-4 as well.

Classical field theory, symmetries and conservation laws.

Lorentz invariance, representations, spinors, vectors.

Second quantization, perturbation theory, Feynman diagrams.

Path integration.

Quantization of QED, calculation of some tree level S-matrix elements.

One-loop renormalization of QED.

These two chapters will be covered for sure:

-- Renormalization:

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).

Books in order of relevance for the course:

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

There will be regular assignments during the semester and a final project.