PHY 610 & 611, Quantum Field Theory I & II

Fall 2012 (N4006 Melville) - Spring 2013 (P 122), TuTh 8:30-9:50

Warren Siegel

office consultation available on request


Different instructors cover different material in this course. (Nobody can teach/learn it all in one year.) Even the basic topics may be taught differently. So it might be worth taking this again if you took it elsewhere, or sitting in if you took it here (or plan on taking it again later).


Physics: standard 1st-semester graduate --
  1. PHY 501 (mechanics): Hamiltonians and Lagrangians, symmetries, relativity
  2. PHY 505 (E&M): Lagrangian, gauges, relativity, Green functions
  3. PHY 511 (QM): more Hamiltonians, spin, statistics, Hilbert space
Mathematics: undergraduate --
  • Gaussian integrals
  • multiplication of 2x2 matrices
  • no level of rigor

Have you already had field theory?

If you learned only QED (or worse yet, just scalar field theory), or just Feynman diagrams, or you used only canonical quantization (which is never used for field theory in research papers anymore), you took a 1960's field theory course. The present course includes required modern topics:
  • Yang-Mills ❤
  • Higgs
  • Standard Model
  • path integrals ❤
  • background fields ❤
  • Faddeev-Popov ghosts ❤
  • anomalies ❤

Field theory's useful for other subjects

This course is oriented toward particle physics, but field theory is often applicable to other areas of physics, like:
  • astrophysics/cosmology
  • nuclear
  • condensed matter
In particular, a currently popular new approach to the latter 2 topics is the anti-de Sitter/conformal field theory correspondence, which makes use of both field theory (especially supersymmetry & conformal symmetry) and string theory.

Have you really had field theory?

Even all the above guarantees only a 1970's course. (Welcome to the 21st century!) You get more in this course than elsewhere:
  • conformal symmetry ❤
  • supersymmetry ❤
  • relativistic mechanics ❤: classical antiparticles, 1st-quantization
  • BRST ❤
  • explicit Yang-Mills amplitudes: spinor helicity
  • renormalons
  • 1/N expansion ❤
  • finite theories

Are you interested in string theory?

This course is not research level, but intended to include all the material prerequisite to more-specialized courses in theoretical high-energy physics.

E.g., this is not a string theory course. But if you plan on doing strings, and think you don't need to learn particles, think again: String theory requires understanding standard field theory topics like all the stuff listed on the left with a "❤". Some of these will be briefly reviewed in our string theory course, but string theory is hard enough if you know field theory, so why make it harder?

Textbook: FIELDS, most of --

First semester ("Part One"): symmetry
  1. Global: Lie algebra, CPT, conformal, Young tableaux, color/flavor
  2. Spin: spinor notation, field eqs., twistors, helicity, supersymmetry
  3. Local: classical pair creation, Yang-Mills
  4. Mixed: chiral, Higgs, Standard Model, GUTs, super models
Second semester* ("Part Two"): quanta
  1. Quantization: path integrals, Wick rotation, S-matrix, F. rules
  2. Quantum gauge theory: BRST, gauges, amplitudes, supergraphs
  3. Loops: Dimensional renormalization, renormalons, 1/N expansion
  4. Gauge loops: asymptotic free., finite theories, anomalies, partons
*Some of this will probably fit into the end of the first semester.

See also an overview of the course.



Grading will be based entirely on homework. Problems will be taken from those in Fields (including the additions on my web page). 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 (or by email).

Auditors are encouraged to try the homework.

University-required statements: These statements are required in all University syllabi. (They are the same in all course syllabi, so just read it once.)