Quantum Field Theory (523-001, 16810)

Fall 2006 Tuesdays and Thursdays from 17:30 to 18:45 in room 184

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. The principal topics will be:
Relativistic Quantum Mechanics
Scattering and the Cluster-Decomposition Principle
Quantum Fields and Antiparticles
The Feynman Rules
The Canonical Formalism
Quantum Electrodynamics
Path-Integral Methods
The Standard Model

The textbook is The Quantum Theory of Fields, Vol. I: Foundations, by Steven Weinberg (Cambridge University Press 1995, reprinted with corrections 1996, 1998, 1999, 2000, 2002, 2003, & 2004 & 2005, ISBN 0-521-55001-7). The bookstore will carry it but probably at a high price and in an old printing, so I suggest ordering it elsewhere, such as Amazon. For those who have an earlier printing of this book or of volumes II and III, here are my files of typos for volume I, volume II, and volume III.

The first chapter of Weinberg's book is on the history of quantum field theory.
Students should read this chapter before or shortly after the start of classes.

Here and here and here and here and here and here are my notes for chapters one and two.

Here and here and here and here and here and here and here and here and here and here and here and here are my notes for chapter three.

Here and here and here are my notes for chapter four.

Here and here and here and here and here and here and here and here and here and here and here and here and here and here and here are my notes for chapter five.

Here is what is intended to be a pedagogical article about spin-one-half fields.

Here and here and here and here and here and here and here and here and here are my notes for chapter six.

Here are some remarks on the momenta of internal lines in Feynman diagrams.

Here is a solution to problem 6.2.

Here are my notes on functional derivatives.

The course grade will be based entirely (and generously) on the homework assignments.

Homework: Do problems 2.1 and 2.2 by September the 12th. Also, show that the special L(p) defined by Eq.(2.5.24) is a Lorentz transformation, that is, it satisfies Eq.(2.3.5). Also, prove Eq.(2.5.31). Also, let p_x = (p,0,0,p⁰) be a momentum in the x-direction. Suppose Ψ_{p_x} = |p_x> is a state of a spin-zero particle moving in the x-direction. To lowest order in the small angle a, find (Ψ_{p_x}, exp(ia J₃) Pⁱ exp(-ia J₃) Ψ_{p_x}), which will be proportional to δ³(0).  Solutions to problems 2.1 and 2.2.

Homework: Do problem 3.1 by September the 21st.  Solution to problem 3.1.

Homework: Do problem 6.1 by midnight on Hallowe'en -- or is that too soon?  Solution to problem 6.1.