Book
This page contains work in progress chapters for a book
based on the Phy396T lecture notes.
Working title is:
Relativistic and Quantum Symmetry Groups
If you have any comments, corrections, suggestions, I would be
most interested in hearing them. Email, scans, marked up copy by
paper mail - whatever works.
Access is restricted. If you would like to have access and
are willing to provide review comments, please contact me at
Stephen
Low email
Chapters 2-5 Release I0.2 Updated June 2, 2010
Chapter 14, Release II0.32 Updated Aug 14, 2010
Chapter 2: Basic Properties of Lie Groups
Chapter 3: Matrix Group Examples
Chapter 4: The Weyl-Heisenberg Group
Chapter 5: Symmetry Group of Hamilton's Mechanics
Chapter 14: Mackey Theorems (includes the Weyl-Heisenberg and Euclidean group examples)
Comments requested on any or all of the following topics:
Content:
Level, readability
Are there sections that are not clear or missing
Scrutiny of all propositions and definitions
Typesetting:
Please note table of contents is a placeholder
Please note the following known problems:
Header numbers dropped when at top of page (pdf driver issue)
Mathematica has trouble with hyphenation (wolfram working)
Don't worry too much about spaces between words from automatic justification at this point - these change with each edit.
PHY396T Course
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
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.
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 bibliography 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, Annals 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.
