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

Differences

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).

Prerequisites

Physics: 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, 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

Global: Lie algebra, CPT, conformal, Young tableaux, color/flavor
Spin: spinor notation, field eqs., twistors, helicity, supersymmetry
Local: classical pair creation, Yang-Mills
Mixed: chiral, Higgs, Standard Model, GUTs, super models

Second semester* ("Part Two"): quanta

Quantization: path integrals, Wick rotation, S-matrix, F. rules
Quantum gauge theory: BRST, gauges, amplitudes, supergraphs
Loops: Dimensional renormalization, renormalons, 1/N expansion
Gauge loops: asymptotic free., finite theories, anomalies, partons

*Some of this will probably fit into the end of the first semester.

Organization

QFT is a big subject; we'll cover a lot of material to give you @ least some exposure to the main ideas.
A theory course, not "theory for ..."; for a more phenomenological alternative/complement, try Elementary Particle Physics (557).
A one-year course: If you plan to take only the first semester as a light meal, you will miss the "main course".
Difficult homework problems, discussed in gory detail in class. (This isn’t a seminar.)
Study the material of each lecture before it’s given, to prepare questions.

Grading

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.)