Physics 223B, Fall 2006 (CRN 37512),  Time: MW 2:10-3:30pm; Place: 416 Phys/Geo
Teacher: Professor Ling-Lie Chau
Office: 431 Phys/Geo; phone: 752-2715;
Office hours: MWF 3:30-4pm -- extendable, at 431 Phys/Geo; or by appointment
Group Theory for the Fundamental Laws of Physics

Motivation: Toward the end of the 20th century physicists (theorists and experimentalists) had consolidated the amazing realization that Nature makes use of group theory for all four basic interactions: weak, electromagnetic (now unified to be called electroweak), strong, and gravitational. Symmetry lays the foundation of physical laws with simplicity beauty. Symmetry breaking brings about the complexity beauty of physical phenomena: mass genesis in particle physics, and critical phenomena and phase transitions in cosmology, condensed matter, sciences of complex systems. Group theory is the precise language to describe them. Therefore, it is important that all physicists understand group theory from this perspective. In this course I will make it clear and precise

Prerequisite of the course:  vector spaces, complex analysis, ODE, PDE, and variation method.

Outline of possible course material:
    1.   Lie Groups in Defining Spaces: Abelian, SO(N), & SO(N+1)
    2.   Representations of U(1), SU(2), & SO(3)
    3.   Representations of SO(3+1), & Relations to SU(2) & SL(2,C)
    4.   SU(3), SU(N), & Particle Cataloging
    5.   Inhomogeneous Groups: ISO(n) & ISO(n+1)
    6.   Lie Groups in Function Spaces
    7.   Heisenberg, Schroedinger, Dirac Equations, & Lie Groups
    8.   Maxwell, Yang-Mills Equations, & Lorentz, Gauge Symmetries
    9.   Einstein Equations & Coordinate & Gauge Symmetries
    10.  Variational Methods
    11.  Global Groups & Applications
    Appendix: Highlights of important prerequisite material .

These are essentially the topics taken from the book I have been writing (with the same title as this course). Needless to say, we will not have time to cover them all. The strategy I will take is to cover the basics in depth, so after taking the course students will be equipped with the basic understanding of group theory and able to add to it whatever more are needed in their research.

Homework                                                                      40%
Midterm 1   (1hr, Wednesday, 11/1/06, class time)          15%
Midterm 2   (1hr, Wednesday, 11/22/06, class time)        15%
Final            (2 hrs, Tuesday, 12/12/06, 130-330pm )      30%
Participation                                                                     Bonus points for grade uplifting

Organizational matters:
* This is a lecture-based course. Lectures are self-contained and sufficient for doing homework and taking the exams of the course. Exams are based upon lectures and homework materials. (Homework and exams are closely related to lectures. So every lecture can be viewed as a homework and exam solving session. Full concentration in listening to lectures and taking lecture notes will save students’ time in doing homework and in preparing for exams.) Therefore, it is essential that students attend the lectures and take good notes, then review and restructure their own derivation, outline and conclusion. Students are encouraged to form study groups for reviewing lectures and discussing them.

[This lecture-based method was created out of necessity due to the lack of a suitable textbook -- and my book material is not ready for distribution. It turns out this method has  many advantages over the conventional method of having a designated textbook.  It saves students time and money, and takes away textbooks as “crutches and excuses ” for the students to not pay full attention to the lectures or even not to come to classes (and then not to read textbooks systematically) and  for the teacher to not be clear and precise in lecturing. In any case this is the best we can do now. At the end of this syllabus, some references are listed.]

* If a student has to miss a class, which should by all means be avoided, it is the student’s responsibility to make arrangements with other students to obtain the lecture notes. However, one should remember to return favors. Collaboration works only when there is give-and-take. Students are encouraged to help other fellow students. (One of the best ways to learn is to teach and help others.)

* Participation will take into consideration various kinds of participation (which are open for your creative implementation). Besides during class and office hours, students are most welcome to ask questions by e-mail. E-mail provides a very efficient form of communication. We should all make the best use of it. I will respond as soon as possible. Those e-mail communications that are relevant and helpful to the whole class will be sent to the whole class. (Students should always specify if they want any of their communications to be kept confidential.) Check e-mail frequently, at least once a day. Please always start the Subject of your e-mail to me by “223B; ----” and then put a few words to capture the content of your e-mail. These will be useful for my filing and making reference to them.

* Bonus points are offered for outstanding homework, exams, active participation (in class, in office hours, or by e-mails) and homework chosen as class solution. (Bonus points to a worthy verbal active participation will be given when it is backed up by an e-mail from the student to me.) Bonus points will be counted toward the score of homework and also be listed separately as an honor and distinction to be counted toward Participation. The quantitative weight of bonus points will be fairly small, however their importance is in their distinction. All bonus points and other participation records will be useful toward possible grade up-lifting.
* Grading will be decided both “absolutely” and “relatively”:  There is a certain absolute standard of the course, above which one passes and below which one fails. Also there is certain absolute standard, above which one gets an A+. Therefore, in principle all of you can get an A or A+. (It did happen.) The grading will also make sure that the better performing students obtain better grades, so the grading is also “relative.”

* This is a 3-unit course. Students need to put in the total about 9-to-12  hours/week for 223B, according to university rules. I would recommend students to spend the 9-to-12 hours/week as follows:
         ** Attending lectures: 3 hours (3x50mins class plus 3x10mins overhead time)
         ** Studying and reorganizing notes: 2-to-3  hours (2x1.5 hours)
         ** Doing homework: 4-to-6 hours.
If students do all of the above, it will be impossible for students to not obtain a good grade. Not only is it the most effective way, it is the most enjoyable way. The methodology will serve the students well no matter what they endeavor to do.

* There will be 10 homework, due before the Tuesday class. Every student can discard the worst score, or not to hand in one. No late homework will be accepted, except for, only for, the student’s own dire health-related emergency. In that case, the student must obtain an official letter from a verifiable M.D. who certifies that the student’s health conditions (no specifics needed) are such that the student absolutely cannot do the homework before the due time. Whether a late homework is accepted will be determined on a case-by-case basis. A percentage of the late homework score may be deducted. The precise percentage of the deduction will also be decided on a case-by-case basis. Also understand that once the solution is out, no late homework can be considered, period. For further info, see  Homework Guidelines .

* Graded homework will be in each student's Physics Department mailbox, or in an envelope in front of my office for those who do not have a mailbox in the Physics Department.

* Solutions to the homework will be chosen from students’ solutions. Bonus points will be given to those whose solutions are chosen. A copy of the solution will be delivered to Shields (and students will be notified by e-mail as soon as that happens). The hard copy will be available as a 2hr loan at the Reserve of Shields Library, as well as on the Reserve web.

* Exams are “closed book." Paper will be provided and only those can be used. Therefore, for exams, all that students have to bring are their favorite writing utensils and a well-prepared, clear mind (for which sufficient sleep is absolutely essential). Only, and only, a student’s own dire health-related emergency can allow the student to miss an exam. In that case, the student must obtain an official letter from a verifiable M.D. who certifies that the student’s health conditions (no specifics needed) are such that the student absolutely cannot come to take the exam. Whether a make-up exam  is granted will be determined on a case-by-case basis. A percentage of the make-up exam score may be deducted. The precise percentage of the deduction will also be decided on a case-by-case basis.

* Any corrections or rebuttals to graded homework must be done in writing and given with the full graded homework to me  before the first class of the following week . I will answer them in writing. The same procedure applies to graded exams, except that the deadlines for exam rebuttals are within 24 hours.

References (2hr loan at Reserve of Shields for this course)
* H.F. Jones, Groups, Representations, and Physics
* W.K. Tung, Group Theory in Physics

Useful tables (available for use at the libraries):
* Tables of Integrals and Other Mathematical Data, H.B. Dwight,Macmillan;
* Tables of Integrals, Series and Products, I.S. Gradshteyn and L.M.Ryzhik, Academic Press;
* Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Editors M. Abramowitz and I.A. Stegun, National Bureau of Standards;
* Encyclopedic Dictionary of Mathematics, Mathematical Society of Japan.