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Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories.
1909
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by same author, On holomorphic factorization of WZW and coset models , Comm. Math. Phys. 144
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Daniel S. Freed and Frank Quinn, Chern-Simons theory with finite gauge group , Comm. Math. Phys. 156
1993
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John C. Baez and James Dolan, Higher-dimensional algebra and topological quantum field theory , J. Math. Phys. 36
1995
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1995
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by same author, Characteristic numbers and generalized path integrals , Geometry, topology, & physics, Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, 1995, pp. 126–138. arXiv:dg-ga/9406002
1995
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by same author, The Verlinde algebra and the cohomology of the Grassmannian , Geometry, topology, & physics, Conf. Proc. Lecture Notes Geom. Topology, IV, Int. Press, Cambridge, MA, 1995, pp. 357–422. arXiv:hep-th/9312104
1995
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Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison, and Edward Witten (eds.), Quantum fields and strings: a course for mathematicians. Vol. 1, 2 , American Mathematical Society, Providence, RI, 1999. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997
1997
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Pierre Deligne and Daniel S. Freed, Classical field theory , Quantum Fields and Strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 137–225
1999
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by same author, Dynamics of quantum field theory , Quantum fields and strings: a course for mathematicians, Vol. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 1119–1424
2011
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2011
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2011
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by same author, Toward Topological Classification of Phases with Short-range Entanglement , 2011. http://online.kitp.ucsb.edu/online/topomat11/kitaev/ . Lecture at KITP
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1999
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by same author, Unpaired Majorana fermions in quantum wires , Physics-Uspekhi 44
2001
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Ib Madsen and Ulrike Tillmann, The stable mapping class group and Q ( ℂ ℙ + ∞ ) Q(\mathbb{C}\mathbb{P}^{\infty}_{+}) , Invent. Math. 145
2001
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H. Endo, M. Korkmaz, D. Kotschick, B. Ozbagci, and A. Stipsicz, Commutators, Lefschetz fibrations and the signatures of surface bundles , Topology 41
2002
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Allen Hatcher, Algebraic topology , Cambridge University Press, Cambridge, 2002
2002
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Graeme Segal, The definition of conformal field theory , Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, Cambridge, 2004, pp. 421–577
2004
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M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M-theory , J. Diff. Geom. 70
2005
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Daniel S. Freed and Gregory W. Moore, Setting the quantum integrand of M-theory , Commun. Math. Phys. 263
2006
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by same author, Anyons in an exactly solved model and beyond , Annals of Physics 321
2006
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2011
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by same author, Felix Klein Lectures 2011 . http://www.mpim-bonn.mpg.de/node/3372/abstracts
2011
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2012
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2013
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Daniel S. Freed, The cobordism hypothesis , Bull. Amer. Math. Soc. (N.S.) 50
2013
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2013
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by same author, On the Classification of Short-Range Entangled States , June, 2013. http://scgp.stonybrook.edu/archives/7874 . Lecture at SCGP
2013
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2013
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Terence Tao, Compactness and contradiction , American Mathematical Society, Providence, RI, 2013
2013
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2013
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by same author, The Chern-Simons functional in condensed matter physics . http://videostreaming.gc.cuny.edu/videos/video/792/in/channel/55/ . Lecture at CUNY graduate center, May, 2013
2013
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2014
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Daniel S. Freed and Constantin Teleman, Relative quantum field theory , Comm. Math. Phys. 326
2014
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2014
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by same author, Short range entangled quantum states , May, 2014. lecture at MSRI
2014
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2023
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