"Seminar topics on affine Lie algebras"의 두 판 사이의 차이

2020년 11월 16일 (월) 04:28 기준 최신판

memo

http://books.google.com.au/books?id=_0zyWYJGUakC&printsec=frontcover&dq=Application+of+group+theory+in+physics+and+mathematical+physics&source=bl&ots=q5F83jIVbm&sig=ii3X3aeugpTZMFa1DfiGnPOkPSc&hl=en&ei=1FIwTNiXN5SSjAf_0PCWBg&sa=X&oi=book_result&ct=result&redir_esc=y#v=onepage&q&f=false

future topics

admissible representations of affine algebras
Heisenberg algebra
W-algebra
Feigin-Frenkel isomorphism
KZ equation
quantum affine algebra
Shapovalov form
vertex algebra
loop groups and positive energy representation
free field realization
- \(b-c\) ghost systems
- \(\beta-\gamma\) ghost systems
- free bosons - Heisenberg

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-This is the webpage for the seminar on Affine Lie Algebras for Semester 1 2015 at the University of Queensland . The goal is to understand various aspects of the theory useful in both mathematics and physics.
-Meetings: Thursdays 3-4:30 pm, Priestly Building Seminar Room 67-442
-INVITATION EMAIL SENT TO EVERYBODY IN MATH AND PHYSICS
-Dear colleagues,
-We are having a seminar on Affine Lie Algebras this semester. The goal is to understand various aspects of the theory useful in both mathematics and physics. The seminar will meet once a week on
-Thursdays 3:00-4:30 pm - Priestly Building 67-442.
-The first meeting will be this coming Thursday (March 1).
-This is a continuation of the seminar we had last semester regarding mathematical aspects of quantum field theory. Following the approach of the last semester, most of the talks will be given by students and on voluntary basis. The talks will be of informal nature, with lots of questions and discussions. New postgraduate students who are interested in the topic are especially encouraged to participate. We hope to continue to have the presence of the more knowledgable staff to guide us through the intricacies of the subject.
-The program of the seminar can be found at:
-https://sites.google.com/site/masoudkomi/research/qft
-This is the only email sent to the mass email list regarding this semester's seminar. If you are not already on the seminar's list and would like to be informed, please send me an email and I will include you in the future announcements.
-All the best,
-==topics==
-===Kac-Moody algebras===
-* chapter 1&4 of <ref name="kac" />
-===affine Lie algerbas as central extensions of loop algerbas===
-* chapter 7 of <ref name="kac" />
-===Sugawara construction of Virasoro algebra===
-===integrable highest weight representations of affine Lie algebras===
-===Wess-Zumino-Witten model===
-* Walton, Mark. ‘Affine Kac-Moody Algebras and the Wess-Zumino-Witten Model’. arXiv:hep-th/9911187, 23 November 1999. http://arxiv.org/abs/hep-th/9911187.
-===modular transformations of characters of affine Lie algebras===
-* Macdonald, I. G. 1981. “Affine Lie Algebras and Modular Forms.” In Séminaire Bourbaki Vol. 1980/81 Exposés 561–578, 258–276. Lecture Notes in Mathematics 901. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0097202.
-* chapter 4 of <ref name="wakimoto" />
-===fusion rules and Verlinde formula===
-* Gannon, Terry. 2005. “Modular Data: The Algebraic Combinatorics of Conformal Field Theory.” Journal of Algebraic Combinatorics. An International Journal 22 (2): 211–250. doi:10.1007/s10801-005-2514-2.
-* Feingold, Alex J. 2004. ‘Fusion Rules for Affine Kac-Moody Algebras’. In Kac-Moody Lie Algebras and Related Topics, 343:53–96. Contemp. Math. Amer. Math. Soc., Providence, RI. http://www.ams.org/mathscinet-getitem?mr=2056680. http://arxiv.org/abs/math/0212387
-* Fuchs, J. 1994. ‘Fusion Rules in Conformal Field Theory’. Fortschritte Der Physik/Progress of Physics 42 (1): 1–48. doi:10.1002/prop.2190420102. http://arxiv.org/abs/hep-th/9306162
-* Verlinde, Erik. 1988. “Fusion Rules and Modular Transformations in 2D Conformal Field Theory.” Nuclear Physics B 300: 360–376. doi:[http://dx.doi.org/10.1016/0550-3213(88)90603-7 10.1016/0550-3213(88)90603-7].
-===vertex operator constructions of basic representations===
-* Frenkel, I. B., and V. G. Kac. ‘Basic Representations of Affine Lie Algebras and Dual Resonance Models’. Inventiones Mathematicae 62, no. 1 (81 1980): 23–66. doi:10.1007/BF01391662.
-===future topics===
-* admissible representations
-* Heisenberg or Virasoro?
 ==memo==
 * http://books.google.com.au/books?id=_0zyWYJGUakC&printsec=frontcover&dq=Application+of+group+theory+in+physics+and+mathematical+physics&source=bl&ots=q5F83jIVbm&sig=ii3X3aeugpTZMFa1DfiGnPOkPSc&hl=en&ei=1FIwTNiXN5SSjAf_0PCWBg&sa=X&oi=book_result&ct=result&redir_esc=y#v=onepage&q&f=false
-==links==
+===future topics===
-* [https://sites.google.com/site/masoudkomi/research/qft UQ Quantum Field Theory Seminar 2013-2014]
+* admissible representations of affine algebras
+* Heisenberg algebra
+* W-algebra
-==references==
+* Feigin-Frenkel isomorphism
-<references>
+* KZ equation
-<ref name="kac">Kac, Victor G. 1994. Infinite-Dimensional Lie Algebras. Cambridge University Press.</ref>
+* quantum affine algebra
-<ref name="fms">Francesco, Philippe, Pierre Mathieu, and David Senechal. 1999. Conformal Field Theory. Corrected edition. New York: Springer.</ref>
+* Shapovalov form
-<ref name="wakimoto"> Wakimoto, Minoru. Infinite-Dimensional Lie Algebras. Vol. 195. Translations of Mathematical Monographs. American Mathematical Society, Providence, RI, 2001. http://www.ams.org/mathscinet-getitem?mr=1793723.</ref>
+* vertex algebra
-<ref name="goddard">Goddard, Peter, and David Olive, eds. Kac-Moody and Virasoro Algebras. Vol. 3. Advanced Series in Mathematical Physics. World Scientific Publishing Co., Singapore, 1988. http://www.ams.org/mathscinet-getitem?mr=966668.</ref>
+* loop groups and positive energy representation
+* free field realization
+** <math>b-c</math> ghost systems
+** <math>\beta-\gamma</math> ghost systems
-===reading for fun===
+** free bosons - Heisenberg
-* Berman, Stephen, and Karen Hunger Parshall. ‘Victor Kac and Robert Moody: Their Paths to Kac-Moody Lie Algebras’. The Mathematical Intelligencer 24, no. 1 (13 January 2009): 50–60. doi:[http://link.springer.com/article/10.1007%2FBF03025312 10.1007/BF03025312].
-* Dolan, Louise. ‘The Beacon of Kac-Moody Symmetry for Physics’. Notices of the American Mathematical Society 42, no. 12 (1995): 1489–95. http://www.ams.org/notices/199512/dolan.pdf
 [[분류:Talks and lecture notes]]
 [[분류:Lie theory]]
+[[분류:migrate]]

"Seminar topics on affine Lie algebras"의 두 판 사이의 차이

2020년 11월 16일 (월) 04:28 기준 최신판

memo

future topics

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