Research/Study Course in Quantum Field Theory

Table of Contents

  1. Latest News
  2. Syllabus
  3. Useful References

Latest News

Most Recent Update: December 13, 2006

I spoke with Professor Goldberg and we agreed to divide some of the course responsibilities between the two of us. We also agreed that the best strategy was to begin with Chapters 2-5 of Peskin & Schroeder and then evaluate where we stand at that point.

Syllabus

This semester-long course is designed to provide an overview of certain key concepts in quantum field theory (QFT). In an ideal world we would begin at the beginning of the Peskin & Schroeder textbook and march through to the end, doing many of the problems and supplementing the material (when possible and necessary) with sections from other texts. Such a procedure would certainly involve more time than a single semester. As instruction of this nature must be tailored to fit the individual students, it is to be expected that some flexibility in the topics covered will be required. What is presented below attempts to provide for a base of knowledge with a selection of additional important topics to be covered if circumstances allow.

Therefore we propose to cover roughly one-half of the text, using a goal-based strategy. Classes will meet once -- or possibly twice -- a week in which some fraction of the time is spent in student presentations of the key concepts for that week. There will be time for questions and faculty instruction, but the bulk of the learning will be self-directed by the students with guidance from the faculty instructors. Satisfactory progress will be indicated both in the presentation of the students as well as by occasional problem assignments (roughly one per week, problems to be chosen from the list below or from similar material).

The primary goals of the course are to understand the following concrete phenomena or bodies of theory (topics in red will be covered if time allows):

  1. The nature of charge-conjugation symmetry and its action on spinors
  2. Origin of Feynman rules: time-ordering of the perturbation expansion, Wick contractions and symmetry factors
  3. The importance of Ward identities
  4. Vertex correction diagrams, culminating in a calculation of the anomalous magnetic moment of the electron
  5. Calculation of vacuum polarization diagrams for QED
  6. The need for regularization of divergent amplitudes: understanding what a renormalization scheme is and how to compare various schemes
  7. The effective action and effective scalar potential
  8. Understand what the renormalization group represents and how to compute beta-functions/anomalous dimensions
  9. Non-Abelian gauge symmetries: basic facts about Lie algebras, why gluons couple to themselves
  10. Faddeev-Popov ghosts
  11. How to compute a basic 2-to-2 QCD amplitude (e.g. g g to q qbar)
  12. What is an anomaly: how to compute anomaly coefficients, why the neutral pion decays to two photons
  13. The Higgs mechanism and the Goldstone theorem
  14. What is "custodial SU(2)"?

Satisfactory performance will be assessed by students completing the following exercises by the end of the semester:

  1. P&S Problem 6.3 [Exotic contributions to the electron g-2 factor]
  2. Computation of the vacuum polarization in QED, computation of QED beta-function and computation of renormalized QED coupling in the MS-bar scheme.
  3. P&S Problem 16.2 [Computation of QED/QCD beta-functions with charged scalars]
  4. P&S Problem 17.3 [Computation of differential cross-section for gluon pair production at a hadron collider]
  5. If time allows: P&S Final Project [SM Higgs decay rates]

For guidance, the material that will be relevant for the above goals is roughly that of the following sections from Peskin & Schroeder. Additional material will be taken from other texts, mostly from the first two sections of the "Useful References" area below.

  1. P&S Chapter 3 -- especially sections 3.3-3.6
  2. P&S Chapter 4 -- especially sections 4.5-4.8
  3. Re-acquaint yourself with QED (P&S Chapter 5)
  4. Optional P&S Chapter 6.2 and 6.3
  5. Optional P&S Chapter 7.5
  6. Optional P&S Chapter 9
  7. P&S Chapter 10.1-10.3
  8. P&S Chapter 11
  9. P&S Chapter 12
  10. P&S Chapter 15
  11. P&S Chapter 17.1-17.4
  12. P&S Chapter 19.1-19.4
  13. P&S Chapters 20 and 21

Useful References

Some references, in roughly the order I found them useful. Many more books (and excellent review articles) exist, and more are published every year...

Quantum Field Theory

Standard Model & Collider Physics

Supersymmetry

Supergravity

General Relativity & Cosmology

String Theory

Mathematics