How to Talk to a Physicist: Groups, Symmetry, and Topology

Course Information

Course syllabus.   (As of 18 Mar 2005.)

Meeting times:
        Tuesdays and Thursdays, 7:00-8:30pm (Note change from Mon to Tue.)
Location:
        Science Center 310.
First Meeting:
        Tuesday, July 5, 7:00-8:30pm.

Textbooks:
        "Geometrical Methods of Mathematical Physics," by Bernard Schutz (more readable)
        "Geometry, Topology and Physics," by Mikio Nakahara (more advanced)
Some project ideas: (pdf)
Lecture Notes:
        Complete lecture notes in a single, 71 page file: (pdf)

        Lecture 1: (5 Jul 05) (pdf) [Includes Exercises 1-8.]
             Suggested Reading: Schutz: 1.4-1.6 (Groups, linear algebra, & matrices); 2.1-2.4 (Basics of manifolds)
                                    or   Nakahara: 2.1-2.2 (Maps & vector spaces); 5.1 (Manifold intro)

         Lecture 2: (7 Jul 05) (pdf) [Includes Exercises 9-15.]
             Suggested Reading: Both Schutz: 3.1-3.4, 3.14-3.17 and Nakahara: 5.2-5.3, 5.6 treat Lie groups and Lie algebras in a much more abstract and technical way than I have in the lectures.

         Lectures 3 & 4: (12 and 14 Jul 05) (pdf) [Includes Exercises 16-22.]
             Suggested Reading: Your favorite quantum mechanics book. I recommend Griffiths or Shankar, below. Look in the index for "spin".

         Lecture 5: (19 Jul 05) (pdf) [Includes Exercises 23-24.]
             Suggested Reading: Most quantum books talk about the Aharonov-Bohm effect; Nakahara's discussion is way more (too?) high-powered. Shankar has a decent chapter about the path integral.

         Lecture 6: (21 Jul 05) (pdf) [Includes Exercises 25-29.]
             Suggested Reading: Nakahara, Chapter 4.

         Lectures 7 & 8: (26 and 28 Jul 05) (pdf) [Includes Exercises 30-43.]
             Suggested Reading: The last section follows Coleman, Section 3 of Chapter 7.

References:
These are the books I have referred to in preparing the lecture notes. Organized roughly in order of increasing difficulty.

"Algebra," by Michael Artin [A good intro to group theory; relevant chapters are Ch.2 (Groups), Ch.3 (Vector Spaces), Ch.4 (Linear Transformations), Ch.8 (Linear Groups)]
"Topology: A First Course," by James R. Munkres [A good intro to topology. The first homotopy group is covered in Chapter 8.]
"Introduction to Quantum Mechanics," by David J. Griffiths [A good first quantum book.]
"Principles of Quantum Mechanics," by R. Shankar [A great intermediate quantum book.]
"Geometrical Methods of Mathematical Physics," by Bernard Schutz [Selected topics in math for physics applications.]
"Modern Quantum Mechanics," by J. J. Sakurai [More advanced quantum book used in the grad course at Berkeley. The explanation of Aharonov-Bohm effect using path integrals came from Section 2.6.]
"Geometry, Topology and Physics," by Mikio Nakahara [Math topics for physics, slightly more sophisticated than Schutz; ignore the useless first chapter.]
"Aspects of Symmetry," by Sidney Coleman [Chapters 6 & 7 discuss homotopy groups and gauge theories.]
"Semi-Simple Lie Algebras and Their Representations," by Robert Cahn [Similar to Georgi; a little more precise but with fewer applications. It's online!]
"Lie Algebras in Particle Physics," by Howard Georgi [Detailed representation theory from a physics point of view with lots of applications.]
"Representation Theory: A First Course," by William Fulton and Joe Harris [High level mathematical approach to group representations.]