Welcome to Physics 507    Spring 2013

Physical Applications of Group Theory

Prof. Steve Sharpe

Tu/Th 11:30 - 1:20  in PAB A110


Index and Links

Office hours and contact information

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The following text is required, and will be used for the part of the course on continuous groups: For the part of the course on finite groups, there will be no required text, since there are many adequate texts that cover this material and you may already have one. If you do not, the following is a (certainly incomplete) list of good options, focusing on relatively inexpensive texts:
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Course Structure and Syllabus

The first part of the course will concern finite groups, the second continuous groups. The split will be approximately 40:60. I will assume no prior instruction in group theory, but will move the course along quite quickly. I'll assume some knowledge of QM, but I expect the course to be accessible to all graduate students, including first years.

I will likely follow closely the syllabus I used when teaching this class in 2009, which can be seen from this link.

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Course Grade

The course grade will depend on the total score on HWs, which all will count about equally, except the last one which may be more extensive.

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Useful links

  • Thanks to Lawrence Yeagley for the link to a (very long!) set of lecture notes on "Applications of group theory to the theory of solids" by Mildred Dresselhaus, which is a precursor to her book (with Gene Dresselhaus and Ada Jorio) on "Group Theory: applications to the physics of condensed matter" (2008, Springer). This goes into great detail on applications to condensed matter.
  • Thanks to Isaac Crosson for the link to the download site for the "Group Explorer" software. This software catalogs and provides details of many of the smaller (mostly order < 20) finite groups.
  • Thanks to Jonathan Diaz this link to the book "Semi-Simple Lie Algebras and their Representations", by Robert Cahn, which (as you can see if you look at the preface) was where I learned this subject. I like the book, but thought that it was out of print. Actually, it turns out that it is now available from Dover Publications at a very reasonable price.
  • Thanks to Jeremy Price for this link to "Lie Groups, Lie Algebras, and Representations", by Brian Hall. This is a nice set of notes that gives a mathematical approach to Lie groups that is written in a way that is accessible to less mathematically inclined physicists. It is a good source for filling in the gaps and substantiating the claims in lectures.
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Stephen Sharpe