PHY 610 & 611
Quantum Field Theory I & II
Fall 2006 (TuTh 11:20-12:40, P123)
Spring 2007 (MWF 9:35-10:30, P128)
office consultation available on request
Summary
Prerequisites
- Physics prerequisites -- standard 1st-semester graduate --
- PHY 501 (mechanics): Hamiltonians and Lagrangians, symmetries, relativity
- PHY 505 (E&M): Lagrangian, gauges, relativity, Green functions
- PHY 511 (QM): more Hamiltonians, spin, statistics
(This stuff will be reviewed, but familiarity is useful.)
- Mathematics prerequisites: undergraduate. Although some unfamiliar with the material might call some of it "abstract" or "mathematical", inspection reveals mostly Gaussian integrals and multiplication of 2x2 matrices, with no level of rigor.
- Nevertheless, the appearance of much "new" material makes this a hard course.
Yet it is suitable for all who are interested in broadening their horizons.
Topics
- The topics covered will be oriented toward particle physics: Although the methods are useful for other areas, we will not cover topics specifically designed for them.
- The subject matter will not be research level, but is intended to include all the material prerequisite to more-specialized courses in theoretical high-energy physics.
- It is a theory course, not "theory for ..."; for a more phenomenological alternative, try Elementary Particle Physics (557).
- This is a modern quantum field theory course: It is not just Feynman diagrams.
- It is not a history course: Topics will be covered in logical order, not chronological.
- It is organized as a one-year course: If you plan to take only the first semester as a light meal, you will miss the "main course".
Outline
We will cover most of the following:
First semester: classical
- Introductory: Lie algebra, CPT, conformal, Young tableaux, color/flavor
- Spin: spinor notation, field equations, twistors, helicity, supersymmetry
- Gauge: classical pair creation, Yang-Mills
- Mixed symmetries: chiral, Higgs, Standard Model, GUTs, super models
This semester is relativistic quantum mechanics and relativistic classical field theory (which are basically the same, by the correspondence principle), including the Standard Model (and a little beyond). Emphasis is placed on symmetries (global and local), which define these theories, and their breaking.
Second semester: quantum
- Quantization: path integrals, Wick rotation, S-matrix, Feynman rules
- Quantum gauge theory: BRST, gauges, amplitudes, supergraphs
- Loops: Dimensional renormalization, renormalons, 1/N expansion
- Gauge loops: asymptotic freedom, finite theories, anomalies, partons
The real quantum field theory is in this semester (at least literally). The emphasis is on evaluation of Feynman diagrams: cross sections, β functions, etc. Choice of methods is based on efficiency, rather than history or beauty --- getting the most answers quickest (without computers).
Textbook: FIELDS
- the textbook for the course (an extended version of my lecture notes), available for free download (also at arXiv.org)
- the latest errata to the text
- comparison to other texts and their various shortcomings (but see Fields for more details and references to supplementary material)
As this book is almost 900 pages, I suggest you try to use it on your computer, or save some trees and print just the bits you need at the time. I recommend the PDF version, which links directly to downloadable reference papers at arXiv.org.
The book has 3 parts: The first 2 parts correspond to the 2 semesters of this course; the third (higher spin --- general relativity, supergravity, etc.) is just for reference.
Grading
Grading will be based entirely on homework. Problems will be taken from those in Fields. You may discuss problems with classmates, but the write-up must be your own. Homework is due one week after assignment, at the beginning of class. (Put it on my desk when you enter.) No late homework is accepted; it may be handed in early, but only to me in person.
University-required statements
These statements are required in all University syllabi. (They are the same in all course syllabi, so just read it once. Apparently, the incorrect use of "impact" as a verb is also required.)