Applications of Lie groups and their representations in relativistic and quantum physics (59801)
The University of Texas at Austin course will be given in the Fall 2009 semester as T/Th 9:30-11:00AM lectures. Room is RLM 14.318.
A syllabus and notes for the course follows
- PHY396 Syllabus (pdf)
- Take home midterm Nov 3-10, No class
Nov 5
- PHY396 Course Notes (Chapter 17-19 Dec 2) ( slides pdf)
- PHY396 Course Notes (Through Chapter 19, Dec 2) (doc pdf)
- Additional figures of Null Surfaces for Chapter 7 (pdf)
- Sketch of Null Surfaces (Mathematica .nb)
- Harvard Gazette:
Researchers
can now stop, start light
The instructor of record for the course is Prof. Gleeson (Associate Chairman of the department). The instructor for the course is Dr. Stephen Low.
Office hours: T/TH 11:00-12:00 and by appointment (just send me email).
For questions, please email me at
The course will be taught from typeset lecture notes as it is a topics course and there is not a single text that covers the material. However, a short bibliograpy is given below for background reading.
For the Introduction to Lie Group theory, the following texts are recommended:
Brian. C. Hall, Lie Groups, Lie ALgebra and Representations, Springer Graduate Texts in Mathematics 222, Springer, New York, 2003.
Robert Gilmore, Lie Groups, Physics and Geometry, Cambridge University Press, Cambridge, 2008.
D.H. Sattinger and O.L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, Applied Mathematical Sciences 61, Springer, New York, 1986
Remarkably, the Weyl-Heisenberg group that is fundamental to quantum mechanics is barely touched in these excellent references and this will be covered in the notes. A more advanced reference that has a good treatment is
Gerald B. Folland, Harmonic Analysis on Phase Space, Annales of Mathematical Studies 122, Princeton University Press, Princeton, 1989
For the representation section, an basic introduction of representations is given in
H.F. Jones, Group, Representations and Physics, Institute of Physics, Bristol, 1998
For projective representations
S. Weinberg, Chapter 2: Relativistic Quantum Mechanics in The Quantum Theory of Fields, Vol 1, University of Cambridge Press, Cambridge, 1995
Mort Hammermesch, Group Theory and its Applications to Physical Problems, Dover, New York, 1989
There is not a straightforward reference for the Mackey theorems and this will be in the notes. The final topics section will be notes with literature references.