imported>Pythagoras0 |
imported>Pythagoras0 |
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| − | This is the webpage for the seminar on QFT at the University of Queensland . We focus on Affine Lie Algebras for Semester 1, 2015. The main goal is to understand various aspects of the theory of affine Lie algebras in mathematics and physics.
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| − | * '''when''' : Thursdays 3-4:30 pm
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| − | * '''where''' : Priestly Building Seminar Room 67-442
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| − | ==topics==
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| − | ===Kac-Moody algebras===
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| − | * chapter 1&4 of [Kac 1994]
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| − | * chapter 14&15 of [Carter 2005]
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| − | ===affine Lie algebras as central extensions of loop algebras===
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| − | * chapter 7 of [Kac 1994]
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| − | * chapter 18 of [Carter 2005]
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| − | ===Sugawara construction of Virasoro algebra===
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| − | * chapter 12 of [Kac 1994]
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| − | * chapter 15 of [FMS 1999]
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| − | ===integrable highest weight representations of affine Lie algebras===
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| − | * chapter 12 of [Kac 1994]
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| − | * chapter 3 of [Wakimoto 2001]
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| − | * chapter 20 of [Carter 2005]
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| − | ===Wess-Zumino-Witten model===
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| − | * chapter 15 of [FMS 1999]
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| − | * 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.
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| − | ===modular transformations of characters of affine Lie algebras===
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| − | * chapter 4 of [Wakimoto 2001]
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| − | * chapter 13 of [Kac 1994]
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| − | * 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.
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| − | ===fusion rules and Verlinde formula===
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| − | * chapter 5 of [Wakimoto 2001]
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| − | * chapter 16 of [FMS 1999]
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| − | * 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.
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| − | * 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://arxiv.org/abs/math/0212387
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| − | * 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
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| − | * 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].
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| − | ===vertex operator constructions of basic representations===
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| − | * chapter 14 of [Kac 1994]
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| − | * chapter 20 of [Carter 2005]
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| − | * 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.
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| − | ===future topics===
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| − | * admissible representations
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| − | * Heisenberg or Virasoro?
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| − | ==links==
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| − | * [https://sites.google.com/site/masoudkomi/research/qft UQ Quantum Field Theory Seminar 2013-2014]
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| − | ==references==
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| − | <HarvardReferences>
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| − | * [*Kac 1994] Kac, Victor G. 1994. Infinite-Dimensional Lie Algebras. Cambridge University Press.
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| − | * [*FMS 1999] Francesco, Philippe, Pierre Mathieu, and David Senechal. 1999. Conformal Field Theory. Corrected edition. New York: Springer.
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| − | * [*Wakimoto 2001] 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.
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| − | * [*Carter 2005] Carter, R. W. 2005. Lie Algebras of Finite and Affine Type. Vol. 96. Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge. http://www.ams.org/mathscinet-getitem?mr=2188930.
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| − | </HarvardReferences>
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| − | ===reading for fun===
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| − | * 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].
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| − | * 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
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| − | * 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.
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| | ==memo== | | ==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 | | * 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 |