PHYS 230b

Instructor: Flip Tanedo (flip.tanedo@ucr.edu / PHYS 3054)

Office Hours: by appointment; usually available Wed 4-5pm

Advanced Quantum Mechanics and Quantum Theory of Fields

4 Units, Prerequisite: Physics 230A or equivalent Tue/Thu 5:00-6:20pm PHYS 2111

Textbook: AQFT Notes by Hugh Osborn, Steffen Gielen, Carl Turner You may also use your favorite quantum field theory textbook.

• See also Romao's AQFT lectures.

We will cover the quantum theory of fields from a functional perspective, renormalization and effective theories, gauge theories and their quantization, and anomalies (as time permits). Material will be inspired by particle physics, but we will focus on general quantum field theories on continuum spacetime.

Syllabus contains all relevant course details, assessment, policies, etc.

Homework

• HW1: Generating Functions (tex)
• HW2: Regularization and Renormalization (tex)

Lecture Notes

1. Path Integrals
   • Lecture 1: Gaussian integrals: probability distributions, moments, generating functions. "Statistical Mechanics"
   • Lecture 2: The partition function as a sum of diagrams, path integral quantum mechanics (stuff we didn't get to)
   • Suggested reading for this week: Osborn section 1, Zee chapter 1. (For discussion of steepest descent, there's a nice, brief paragraph below (14.32) of Schwartz.)
2. Functional Methods: Scalar
   • Lecture 3: the partition function for scalar fields. Suggested reading: Srednicki section 9 (what we did today, in careful detail), section 21 (quantum action)
   • Lecture 4: explicit example with a quartic interaction. We touch on symmetry factors, the exponentiation of disconnected diagrams, the generating functional for connected diagrams.
3. Functional Methods: Fermions, Quantum Action
   • Lecture 5: Fermionic Path Integral. Grassmann numbers.
     • Suggested references: Greiner, Field Quantization (end of the book)
     • Additional references: "Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry," Catto et al., math.stackexchange/1449312 & refs therein.
   • Lecture 6: Quantum Action
     • Suggested references: Srednicki, Banks, Osborn lectures.
4. Loops in QFT: Regularization and Renormalization
   • Lecture 7: Regularization
   • Lecture 8: Renormalization
   • Additional references:
     • Polchinski: Effective Field Theory and the Fermi Surface (TASI 92)
     • Polchinski: Renormalization and Effective Lagrangians, Nucl.Phys. B231 (1984) 269-295 (Notes on section 2 toy model)
     • Polchinski: Memories of a Theoretical Physicist (not about RG, but recommended)
5. Loops in QFT: Renormalization
   • Lec 9: The Callan--Symanzik Equation
     • P. Kraus and D. Griffiths, "Renormalization of a model quantum field theory," American Journal of Physics 60, 1013 (1992)
     • P. Gosdzinsky and R. Tarrach, "Learning quantum field theory from elementary quantum mechanics," American Journal of Physics 59, 70 (1991)
   • Lec 10: Effective Theory and RG
6. EFT and Gauge Theory
   • Lec 11: Effective Theory, Prof. Jose Wudka
   • Lec 12: Introduction to Gauge Theory
   • Other references:
     • Tim Cohen's lectures on EFT
     • Iain Stewart's EFT course
7. Non-Abelian Gauge Theory
   • Lec 13: Gauge fixing: Fadeev-Popov
   • Lec 14: Consequences of Fadeev-Popov
   • Other references:
     • Flip's notes on fiber bundles from grad school
     • Flip's notes on the geometry of BRS and anomalies from grad school
     • R-xi gauge etymology (physics stack exchange)
8. Anomalies I
   • Lec 15: BRST
   • Lec 16: Anomalies: a 2D example
     • Holstein, "Anomalies for Pedestrians," American Journal of Physics 61, 142 (1993)
     • Coon, "Anomalies in Quantum Mechanics: the 1/r2 Potential," American Journal of Physics 70, 513 (2002)
9. Anomalies II
   • Lec 17: Schwinger Model, continued.
   • Lec 18: triangle diagrams
10. Anomalies III and Introduction to the Nonlinear Sigma Model
    • Lec 19: Anomaly cancellation
    • Lec 20: Goldstone bosons, symmetry breaking, the Higgs mechanism