Physics 523 & 524: Quantum Field
M & W 5:30 to 6:45 in room 184,
Instructor: Kevin Cahill
This web-page is arranged with the material of 523 at the top and
of 524 below it.
On the first day of class, we will decide
collectively what book to use as the principal text. There is
Theory of Fields, Vol. I: Foundations
Press 1995, reprinted with corrections 1996, '98, '99, 2000, &
ISBN 0-521-55001-7) is excellent, but he derives everything in
generality and from basic principles. It is therefore a very
book and narrow in scope: he deferred nonabelian gauge theory and
supersymmetry to volumes II and III.
Theory (Cambridge University Press 2007) is broader and
somewhat easier to read, but it skips over the elementary topics too
quickly and tends to bore down too intensely on some subjects.
An early draft of his book is online.
Incidentally, pdf's of scans of many books are
available from Gigapedia.
Pierre Ramond's book
Field Theory : A
Modern Primer is clear and elegant.
Mandl and Shaw's book
has many advantages but uses the old-fashioned Gupta-Bleuler
to quantize the electromagnetic field.
Warren Siegel's book Fields (
The paper "Introductory Lectures on Quantum
Field Theory" by Alvarez-Gaume and Vasquez-Mozo (arXiv:hep-th/0510040v3)
by Peskin and Schroeder An
Introduction to Quantum Field Theory
(Addison Wesley 1995) is a reasonable compromise. Errata in
their book. One possibility
is for me to follow Peskin and Schroeder, adding in some of the
insights available in the other books, especially the ones by
and Srednicki. Another possibility is for me to follow
book, adding in material from Weinberg, etc.
We decided to use the book by Peskin and
Schroeder; I will add extra material from Weinberg, Srednicki,
Zee, and others, as well as from my book
on mathematics for physics graduate students.
Pages 1-27 of class
28-34 of class notes. Extract
from my book on the rotation and
Lorentz groups with the metric switched to that of P&S.
Notes on Wigner rotations and
massive particles and states respond to Lorentz transformations as
as on how spinors must be defined if fields are to respond properly
Poincare' transformations with typos corrected. A few pages from chapter 5 of Weinberg with two
typos corrected. Notes on Schur's
qed. Brief review of the Dirac picture,
called the interaction picture.
Notes on the Feynman propagator.
on Feynman diagrams.
other eight yards on the quantization of
massless vector fields. Notes on massless
particles and fields. Notes on fermion-boson
Informal notes on neutrino oscillations.
photon spin sum.
Notes on the photon propagator.
on electron-positron scattering,
rules for QED, on their
application to e+e- ==> mu+mu-, on traces of gamma matrices, and
how to get the cross-section from the S-matrix amplitude. The
best treatment of Feynman diagrams is in sections 6.1, 6.3, and 8.6
Weinberg's QFTI. Notes on helicity.
scattering. Notes on Compton
scattering. Notes on functional differentiation and
path-integration are in chapters 16 and 17 of my on-line book.
propagator from Coulomb-gauge
QED. Paper on coherent
for fermions. Notes on Yang-Mills
theory. Notes on fermion-antifermion
bosons. Weinberg on the
Video of first lecture.
Video of second lecture.
Video of third lecture.
Video of fourth lecture.
Video of fifth lecture.
Video of sixth lecture. Video of seventh lecture. Video of eighth lecture.
Video of tenth lecture. Video
of eleventh lecture. Video of
lecture. Video of thirteenth
Video of 14th lecture. Video of 15th lecture. Video of first 60 or so minutes of
lecture. Video of
Video of part one and part two of 18th
Video of 19th lecture. Video of 20th lecture. Video of 21st lecture (11/03/10).
Video of 22d lecture (11/08/10).
Video of 23d lecture (11/10/10).
Video of 24th lecture (11/15/10).
Video of 25th lecture (11/17/10).
Video of 26th lecture (11/22/10).
Video of 27th lecture (11/24/10).
Video of 28th lecture (11/29/10).
Video of 29th lecture.
Video of 30th lecture (12/06/10).
1, 2, and 3 of the 31st lecture
(12/08/10). Video of
First homework assignment: Do problems 1
of chapter 2 of P&S. This assignment is due on Thursday,
Sep. 9th. Put it in Zhang's mailbox or send it to him at
email@example.com. Here is a pdf
of chapter 2 of P&S for those who haven't yet gotten a
Solutions to problems 1 and 2 of first homework.
assignment due on Wednesday 29 September. Solutions.
Extra-credit homework assignment: Find the
other lowest-order amplitude S_2 for boson-antiboson scattering by
aping what I did in class. Due Monday 4 October at the start
class; I will do the problem in class.
assignment due on Wednesday 13 October. Solutions.
Fourth homework assignment: For the theory
of a neutral boson interacting
charged fermion, compute the lowest-order S-matrix amplitude
fermion-antifermion goes to two bosons (due Monday 25
Fifth homework assignment: Compute or
write down the lowest-order S-matrix amplitude for the process in
two photons turn into an electron-positron pair (due Monday 1
Sixth homework assignment: Compute or
write down the lowest-order S-matrix amplitude for the process in
two fermions scatter via an SU(2) interaction as described in this assignment. Due Monday 15
Seventh homework assignment: Do problems
of the most recent version of chapter 17 of my book. Due
Wednesday 1 December. Solutions.
Eighth homework assignment: For the
action density on page 12 of my notes on Yang-Mills
theory, show that the action is stationary if the gauge fields
satisfy the equation of motion on page 13 of those
Due Monday 6 December or Wednesday the 8th. Solution.
The last lecture will be on Monday at 5:30 in
unless we somehow can use room 184.
First and second
videos of the first lecture,
19 Jan. 2011, which was a review of gauge theory.
Video of second lecture, 24
on the Faddeev-Popov tricks and ghosts.
Video of third lecture, 24 Jan.,
the Casimir effect.
Video of fourth lecture, 31
on dimensional regularization.
Video of fifth lecture, 7 Feb.,
Video of sixth lecture, 9 Feb.,
the Ward-Takahashi identity.
Video of seventh lecture, 14
on poles in scattering amplitudes.
Video of eighth lecture, 16
on the Yukawa potential and propagators as a poles in scattering
First and second videos of ninth lecture,
Feb., on electromagnetic form factors.
Video of tenth lecture, 23 Feb.,
the anomalous magnetic moment of the electron.
Video of eleventh lecture, 28
on Wilson's formulation of lattice gauge theory.
Video of twelfth lecture, 2
on Wilson's formulation of lattice gauge theory, the case of Z_2,
left-invariant measures on groups, and the Monte Carlo method.
Video of 13th lecture, 21 March,
the renormalization group and the lattice spacing a in SU(N) lattice gauge theory.
Video of 14th lecture, 23 March,
the renormalization group in continuum quantum field theory.
Video of 15th lecture, 28 March,
the renormalization group in continuum quantum field theory and on
Video of 16th lecture, 30 March,
the renormalization group in condensed-matter physics.
Video of 17th lecture, 4 April,
the renormalization group in condensed-matter physics, spontaneous
symmetry breaking, Goldstone's theorem, and the Anderson-Higgs
Video of 18th lecture, 6 April,
spontaneous symmetry breaking, Goldstone's theorem, the
mechanism, grand unification, and the non-relativistic limit of
Video of 19th lecture, 11 April,
the renormalization group in condensed-matter physics, quark
confinement, superfluidity, the Landau-Ginzburg approach to critical
phenomena, and superconductivity.
Video of 20th lecture, 13 April,
the pion as a Nambu-Goldstone boson, and on solitons in
Video of 21st lecture, 18 April,
differential forms and magnetic monopoles.
Video of 22d lecture, 20 April,
solitons, vortices, and magnetic monopoles.
Video of 23d lecture, 25 April,
vortices, forms in Yang-Mills theory, and magnetic
monopoles. This video is incomplete because the camera
out of memory.
Video of 24th lecture, 27 April,
instantons and anyons.
Video of 25th lecture, 2 May, on
abelian and nonabelian Chern-Simons theory and on Hall fluids.
Video of 26th lecture, 4
on the quantum Hall effect.
Video of 27th lecture, 11 May,
electroweak unification and on grand unification.
First homework assignment: (1) Show that the area of a
sphere in d dimensions is 2 pi^(d/2)/Gamma(d/2), which is Weinberg's
(11.2.10). Hint: Compute the integral of exp(-x^2) in d
dimensions using both rectangular and spherical coordinates.
Show that the contribution of the counterterm - (Z_3 - 1) F_ab F^ab
Weinberg's (11.2.15). These equations may be found in the pdf,
Weinberg on renormalization via
Second homework assignment: Do the three problems I discussed
the last class. The first is to
relate Wilson's formula for the
action of a plaquette to the continuum action for a gauge
The second is to do problems (9.23) and (9.24) of my online
The third (for extra credit) is to simulate the Z_2 gauge theory on
5^4 (or bigger) lattice following
Creutz's paper (PRD 21 (1980) 1006.
Solutions to the Wilson-loop and invariant-measure problems.
Third homework assignment: Run Creutz's C code (see below) for
Z_2 lattice gauge theory and produce a rgaph showing strong
hysteresis. For extra credit, modify his code and
graph showing the coexistence of two phases at the critical coupling
beta_t = 0.5* ln(1 + sqrt(2)). Hint: do a cold
and then 100 updates at beta_t, then do a random start and do 100
updates at beta_t. Plot the values of the action against the
update number 1, 2, 3, ...100.
Fourth homework assignment: For extra credit, modify Creutz's
code (see below) for Z_2 lattice gauge theory and vary the
dimension. Show that for d=2, there's no transition; for
d=3, it's a second-order phase transition; and for d = 4, it's a
first-order phase transition. For extra, extra credit,
out and show what happens for d = 5?
Fifth homework assignment: Let A = A_j dx^j be a 1-form.
Let F = dA + A^2 be the Maxwell-Yang-Mills 2-form. Let Q be
trace Tr( A dA + 2A^3/3). Show that dQ = Tr(F^2).
Hint: look at page 4 of my notes on the
My notes on the Casimir effect.
Faddeev-Popov tricks and ghosts.
dimensional regularization. My notes Weinberg's notes on
notes on pi(q^2). Weinberg on polology. My notes on the
renormalization of scalar and spinor fields. My notes on symmetry. My notes on the Ward-Takahashi identity. My
on the conservation of momentum and
charge. My notes on poles in
scattering amplitudes. My notes on Yukawa's
example. My notes on the renormalized
self-energies. My notes on form
factors. My notes on the anomalous
electron. My notes
the renormalization group on the lattice. My notes on the renormalization group in continuum
quantum field theory. My
succinct notes on the renormalization group in continuum
field theory. Chapter 18 of my book
describes the renormalization group. My notes on Nambu-Goldstone bosons. My
notes on the Anderson-Higgs effect.
non-relativistic field theories,
on superfluids, on the Landau-Ginzburg theory of critical
phenomena, and on superconductivity.
the pion as a Nambu-Goldstone
boson. My notes on differential
and magnetic monopoles. My notes on solitons and on vortices
monopoles. My notes on differential
theory. My notes on instantons.
Two of my papers on gauge fields and geometry: I
and II. Two of Wilczek's
papers on anyons: I
and II. My notes
Wilczek's anyons. My notes
on Chern-Simons theory. Zee
on electroweak and grand
Michael Creutz's talk on Z_2.
His C code for Z_2 gauge theory.
His makefile. His C++
theory. His papers PhysRevLett.42.1390
An article that may be of interest or
may be just an effort to attract attention to the Perimeter
Possible discovery of a new particle
mass of about 140 GeV at FNAL.