Here is some basic information about this web page. (This web page is under sonctruction - last update: April 24, 2009.)
I created this web page in the January of 2009 for a seminar at Iowa State University. You can look at the seminar announcement: Announcement. This seminar should be of interest to students and researchers in mathematics, physics, chemistry, and engineering. Students can get credit for this seminar/course.
This seminar meets weekly at 1:10 on Thursdays in Carver Hall Room 0018.
We are concerned with the relationship between group theory and physics. In particular, we are discussing the following book: S. Sternberg, "Groups theory and physics", Cambridge University Press, 1994. You can look at the current list of notes: Notes.
Here is a list of the seminar talks.
April 30: Ken Driessel, "Wigner's classification of the representations of the Poincare group"
Abstract: We shall discuss Wigner's classification of the irreducible representations of the Poincare group. The Poincare group is the group of isometries of Minkowski space-time. It is the full symmetry group of any relativistic field theory. As a result, all the elementary particles fall in representations of this group. Y.S. Kim regards Wigner's work on the Poincare group as "the most fundamental papers in physics". (See, Kim, Y.S. (1996) 'Wigner's last papers on spacetime symmetries' in the Proceedings of the IVth Wigner Symposium 1995 and Kim, Y.S. (1996) 'Wigner's influence on particle physics', Acta Physica Plonica B Vol. 27.) Sternberg writes "All of the recent theories of elementary particles have been shaped by [Wigner's work on] the classification of the irreducible representations of [the Poincare group]. It is difficult to overestimate the importance of this [work] which will certainly stand as one of the great intellectual achievements of the [twentieth] century."
April 23: Ken Driessel, "Induced representations and principle bundles (continued)"
April 16: Ken Driessel, "Induced representations and principle bundles"
Abstract: We continue discussing Chapter 3 "Molecular vibrations and homogeneous vector bundles" in Sternberg's book.
April 9: Ken Driessel, "Molecular displacements and vector bundles"
Abstract: We begin discussing Chapter 3 "Molecular vibrations and homogeneous vector bundles" in Sternberg's book.
April 2: Ken Driessel, "Action on function spaces and the regular representation"
Abstract: We shall continue discussing Chapter 2 "Representation theory of finite groups" in Sternberg's book.
March 26: Ken Driessel, "Schur's lemma and characters"
Abstract: We shall continue discussing Chapter 2 "Representation theory of finite groups" in Sternberg's book.
March 19: Ken Driessel, "Representation theory of finite groups (continued)"
Abstract: We shall continue discussing Chapter 2 "Representation theory of finite groups" in Sternberg's book.
March 12: Ken Driessel, "Representation theory of finite groups"
Abstract: We shall begin to discuss Chapter 2 "Representation theory of finite groups" in Sternberg's book.
March 5: Ken Driessel, "Classification of the finite subgroups of O(3)"
Abstract: We shall continue to discuss Chapter 1 "Basic definitions and examples" in Sternberg's book.
February 26: Ken Driessel, "Some relations between groups important in physics"
Abstract: We continued to discuss Chapter 1 "Basic definitions and examples" in Sternberg's book. You can look at some typed notes connected with this meeting: Group Actions.
February 19: Ken Driessel, "Some groups important in physics"
Abstract: We began discussing Chapter 1 "Basic definitions and examples" in Sternberg's book.