Physics 883 Course notes

Class notes for Quantum Field Theory I.
The notes are divided by chapter in Mandl and Shaw.
They are stored as .pdf files and are about 1 MB each.

• Chapter 1 Quantization of the electromagnetic field: a preview of QFT.
• Chapter 2 Lagrangian field theory.
• Chapter 3 The Klein-Gordon field.
• Appendix A The Dirac equation. [The first few pages are messy, but after pg. A202 become legible. Note that the page numbering here is unrelated to that of the main lecture notes.]
• Chapter 4 Quantization of the Dirac field.
• Chapter 5 Covariant quantization of the electromagnetic field.
• Chapter 6 Interacting fields: the S-matrix expansion and Wick's theorem.
• Chapter 7 Feynman diagrams and rules in QED.
• Chapter 8A Fundamental processes: phase space integration; spin sums and trace theorems; e- e+ -- mu- mu+; e- e+ -- quark + antiquark.
• Chapter 8B The Ward identity; Current conservation and virtual photons.
• Chapter 8C+8D Rutherford scattering (8C); Old fashioned perturbation theory for Compton scattering (8D).

Physics 882 Course notes

This is a temporary location for class notes for Quantum Field Theory II.
The notes are generally divided by section number according to Peskin and Schroeder.
One section constitutes an independent introduction to the V-A theory of the weak interactions.
Various subsets of these notes were used in several incarnations of this course.

• Chapter 6.2 The Electron Vertex Function: Formal Structure (pp. 1-16).
• Chapter 6.3 The Electron Vertex Function: Evaluation (pp. 17-38).
• Chapter 7.1A The Electron Self-Energy: Mass and Wave Function Renormalization, and The (One-Loop) Ward-Takahashi Identity (pp. 39-63).
• Chapter 6.4, 6.1 Soft Photons and The Infrared "Catastrophe" (pp. 64-77).
• Chapter 7.5A Evaluation of the Photon Self-Energy: Dimensional Regularization (pp. 78-98).
• Chapter 7.5B Physics of the Photon Self-Energy: Charge Renormalization and the Running Coupling; The Lamb Shift; Equivalence of Dimensional and Pauli-Villars regularizations (pp. 99-119).
• Chapter 10.1 Systematics of Renormalization: Superficial Degree of Divergence; Primitively Divergent Amplitudes in QED; Renormalizability and ``Dimensional Analysis'' (pp. 120-144).
• Chapter 10.2-10.5 Renormalized Perturbation Theory in Phi^4 Theory and in QED; Renormalization Beyond One-Loop Order; Partial Calculation of the Two-Loop Renormalization of Phi^4 Theory (pp. 145-171).
• Chapter 9.1 Path Integral for One-Dimensional Quantum Mechanics (pp. 172-182).
• Chapter 9.2 Path Integral for Scalar Field Theory: The Generating Functional, The Free Field Propagator, and Feynman Rules for Phi^4 Theory (pp. 183-200).
• Chapter 9.4,9.5 Functional Quantization of the Photon Field, and the Faddeev-Popov Procedure; Functional Quantization of the Dirac Field, and Feynman Rules in QCD (pp. 201-220).
• Chapter 12 The Renormalization Group: Wilson's Approach to Renormalization Theory; Integrating Out UV Fluctuations and Construction of The Effective Lagrangian; Renormalization Group Flows.
• Chapter 15 Non-Abelian Gauge Invariance.
• V-A Theory Introduction to the Weak Interactions.
• Chapter 20 Gauge Theories with Spontaneous Symmetry Breaking.
• Chapter 16 Quantization of Non-Abelian Gauge Theories.