Weekly Agenda

Week 1-2: Path Integral

Correlation functions, S-matrix elements, the LSZ formalism. Reading off Feynman rules from an action. Fermionic variables.  

Homework

Week 3-4: Renormalization

Dealing with divergences, "dimensions change when you change dimensions," β function, Wilsonian effective field theory and theory space, Kallen-Lehmann spectrum.

• "Renormalization and Effective Lagrangians," Joseph Polchinski, Nucl.Phys.B 231 (1984) 269-295

• "Effective Field Theory and the Fermi Surface," Joseph Polchinski (hep-th/9210046)

• "Renormalization of a model quantum field theory," Per Kraus;  David J. Griffiths, Am. J. Phys. 60, 1013–1023 (1992)

• "Learning quantum field theory from elementary quantum mechanics, P. Gosdzinsky;  R. Tarrach, Am. J. Phys. 59, 70–74 (1991)

• "Anomalies in quantum mechanics: The 1/r^2 potential,"  Sidney A. Coon;  Barry R. Holstein, Am. J. Phys. 70, 513–519 (2002)

Of historical significance:

• "Memories of a Theoretical Physicist," Joseph Polchinski

Week 5-6: Gauge Theory 

Gauge symmetry versus gauge redundancy. Gauge fixing and the Fadeev-Popov procedure. β function for gauge theories. If time: soft theorems and infrared divergences.

• "Why Gauge?" Carlo Rovelli (arxiv:1308.5599)

• "What does the R stand for in Rξ gauge?" (physics.stackexchange question 434102)

Week 7-8: Anomalies

When a theory is "mathematically wrong." The Fujikawa method. Anomaly coefficients. Chiral fermions. 

• "Anomalies for pedestrians," Barry R. Holstein, Am. J. Phys. 61, 142–147 (1993)

Week 9-10: Symmetry Breaking

Goldstone's theorem, Goldston boson equivalence, electroweak symmetry breaking. How far yoiu can go by just writing out even index explicitly—a.k.a. "group theory without theory."