The course is a continuation of 523, but students may jump in without having taken 523. Students are expected to ask questions in and out of class.

The course is designed for graduate students in physics, especially those in optics, condensed-matter, astro, or particle physics. It will discuss the quantum theory of fields with an emphasis on quantum electrodynamics and the standard model. I plan to do in class many computations of QED cross-sections.

The principal topics will be: The Canonical Formalism, Quantum Electrodynamics, Path-Integral Methods, Renormalization, The Standard Model.

Principle of Stationary Action

The action I is an integral over space-time

I = ∫d

of a Lagrange density L(x), which usually is a function of the fields f

f

with respect to x

L(x) = L( f

(I am avoiding Greek letters, italic fonts, and partial-derivative symbols to save time.)

Principle of Stationary Action

The field equations of both classical and quantum field theories follow from the principle of stationary action. Here is the idea: Suppose that we change the fields f

f

the action changes only in second order (df

f

df

That is the change in the derivative is the derivative of the change.

Let's require that the change dI in the action I be of second order in the changes df

dI = d∫d

in which we sum over all the fields f

Now we integrate the last term by parts, throwing away the surface term because our fields all vanish at large distances:

dI = ∫d

We require that dI vanish for all tiny variations df

0 = (dL/df

Joseph-Louis Lagrange was born on 25 Jan 1736 in Turin, Sardinia-Piedmont (now Italy) and died on 10 April 1813 in Paris, France. At the age of 19, he became professor of mathematics at the Royal Artillery School in Turin. He survived the French Revolution in part because he believed that

Symmetries of the Lagrange Density

Often the Lagrange density L(x) is invariant under a scrambling of the fields among themselves

f

at the same point x. Such a symmetry is called "internal." Each internal symmetry leads to a conserved current j

that is, a combination of the fields and their derivatives that satisfies

0 = j

The invariance of the Lagrange density L(x) implies

0 = (dL/df

Lagrange's equation of motion allow us to write this as

0 = (

So the conserved current j

j

Here are some notes on fermion-fermion, fermion-boson, and boson-boson scattering and on fermion-antifermion scattering and on the solution to Weinberg's problem 6.1.

Here are some notes on sections 7.3 & 7.4 of Weinberg's book.

Here are 66 pages of my notes on Weinberg's chapter 7.

Here are 10 more pages of my notes on chapter 7.

Here are 64 pages of my notes on chapter 8.

To view a video file of a lecture, students should download the file to their computers.

Video (wmv) file of lecture of Monday 29 January 2007 on Feynman diagrams for fermion-boson scattering.

Video of lecture of Wednesday, 31 January 2007 on current conservation, the energy-momentum tensor, and the six currents that are conserved when this tensor is symmetric.

Video of lecture of Monday, 5 February 2007 on Belinfante's symmetric energy-momentum tensor and the formula it gives for the angular-momentum operators. This formula is the basis for understanding the spin of the proton.

Video of lecture of Wednesday, 7 February 2007 on boson-boson scattering.

The lecture of 9 February was snowed-out.

Video of lecture of Monday, 12 February 2007 on fermion-anti-fermion scattering and on boson-boson scattering in the theory of problem 6.1; remarks about cross-sections.

Video of lecture of Monday, 19 February 2007 on the quantization of the theory of a massive vector boson.

Video of the lecture of Wednesday, 21 February 2007 on the quantization of the theory of a Dirac fermion and on constraints--regrettably without audio.

Video of lecture of Monday, 26 Feb. on Dirac brackets.

Video of lecture of Wednesday, 28 Feb. on quantum electrodynamics--regrettably without audio.

The lectures of March 5th and 7th were postponed because of a biophysics meeting; they will be rescheduled. The lectures of March 12th and 14th did not occur because of Spring Break.

First video of lecture of Monday, 19 March, second video, and third video on the use of gauge fixing and Dirac brackets to quantize electrodynamics.

Video of lecture of Wed., 21 March, on the photon propagator and the Feynman rules for QED.

Video of lecture of Mon., 26 March, on Compton scattering.

Video of lecture of Wed., 28 March, on Compton scattering. (tail end of that video)

Notes on Compton scattering.

Video of lecture of Monday, April 2d, on path integrals.

Video of lecture of Wednesday, April 4th, on path integrals.

Video of lecture of Monday, April 9th, on path integrals.

Notes on how to do multiple gaussian integrals.

Video of lecture of Wednesday, April 11th, on path integrals. Unfortunately, the file is very noisy and jerky, probably unusable.

Video of lecture of Monday, April 16th, on fermionic path integrals.

Video of lecture of Wednesday, April 18th, on fermionic path integrals.

Notes on fermionic path integrals.

Video of lecture of Monday, April 23d, on the path-integral formulation of QED.

Video of lecture of Wednesday, April 25th, on poles and renormalization.

Video of lecture of Monday, April 30th, on vacuum polarization in QED.

Notes on shift in the energy of an atomic electron due to vacuum polarization.

Video of lecture of Wednesday, May 2d, on the anomalous magnetic moment of the electron.

Notes on magnetic moments.

Video of lecture of Monday, May 7th, on magnetic moments and on the self-energy of the electron.

Video of lecture of Wednesday, May 9th, on the self-energy of the electron, on the general theory of renormalization, and on infra-red singularities.

Notes on the self-energy of the electron.

Notes on non-abelian gauge theory.

More of same.

Video of lecture of Monday, May 14th, on non-abelian gauge theory.

Notes on Goldstone bosons and the Higgs mechanism.

Video of lecture of Wednesday, May 16th, on the quantization of non-abelian gauge theories, the Faddeev-Popov trick, ghosts, the Feynman rules, Goldstone bosons, and the Higgs mechanism.