Lectures on Topological Quantum Field Theory
Chapter
Abstract
What follows are lecture notes about Topological Quantum Field Theory. While the lectures were aimed at physicists, the content is highly mathematical in its style and motivation. The subject of Topological Quantum Field Theory is young and developing rapidly in many directions. These lectures are not at all representative of this activity, but rather reflect particular interests of the author.
Keywords
Gauge Theory Line Bundle Conjugacy Class Conformal Block Conformal Field Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
- [A]M. F. Atiyah, Topological quantum field theory, Publ. Math. Inst. Hautes Etudes Sci. (Paris) 68 (1989), 175–186.CrossRefGoogle Scholar
- [ABP]M. F. Atiyah, R. Bott, V. K. Patodi, On the heat equation and the index theorem, Invent. math. 19 (1973), 279–330.MathSciNetADSMATHCrossRefGoogle Scholar
- [ADW]S. Axelrod, S. Della Pietra, E. Witten, Geometric quantization of Chern-Simons, gauge theory. J. Diff. Geo. 33 (1991), 787–902.MATHGoogle Scholar
- [APS]M. F. Atiyah, V. K. Patodi, I. M. Singer, Spectral asymmetry and Riemannian geometry. III, Math. Proc. Cambridge Philos. Soc. 79 (1976), 71–99.MathSciNetMATHCrossRefGoogle Scholar
- [C]J. Cheeger, Analytic torsion and the heat equation, Ann. Math. 109 (1979), 259–322.MathSciNetMATHCrossRefGoogle Scholar
- [CS]S. S. Chern, J. Simons, Characteristic forms and geometric invariants, Ann. Math. 99 (1974), 48–69.MathSciNetMATHCrossRefGoogle Scholar
- [DW]R. Dijkgraaf, E. Witten, Topological gauge theories and group cohomology, Com-mun. Math. Phys. 129 (1990), 393–429.MathSciNetADSMATHCrossRefGoogle Scholar
- [DPR]R. Dijkgraaf, V. Pasquier, P. Roche, Quasi-quantum groups related to orbifold, models, Nuclear Phys. B. Proc. Suppl. 18B (1991), 60–72.MathSciNetADSCrossRefGoogle Scholar
- [F1]D. S. Freed, Classical Chern-Simons theory, Part 1,Adv. Math. (to appear).Google Scholar
- [F2]D. S. Freed, Higher line bundles (in preparation).Google Scholar
- [F3]D. S. Freed, Classical Chern-Simons theory, Part 2 (in preparation).Google Scholar
- [F4]D. S. Freed, Locality and integration in topological field theory,Proceedings of the XIX International Colloquium on Group Theoretical Methods in Physics, Ciemat (to appear).Google Scholar
- [F5]D. S. Freed, Higher algebraic structures and quantization (preprint, 1992 ).Google Scholar
- [FG1]D. S. Freed, R. E. Gompf, Computer calculation of Witten’s 3-manifold invari-, ant, Commun. Math. Phys. 141 (1991), 79–117.MathSciNetADSMATHCrossRefGoogle Scholar
- [FG2]D. S. Freed, R. E. Gompf, Computer tests of Witten’s Chern-Simons theory, against the theory of three-manifolds, Phys. R.v. Lett. 66 (1991), 1255–1258.MathSciNetADSMATHCrossRefGoogle Scholar
- [FQ]D. S. Freed, F Quinn, Chern-Simons theory with finite gauge group,Commun. Math. Phys. (to appear).Google Scholar
- [Fr]W. Franz, ‘ber die Torsion einer Überdeckung, J. Reine Angew. Math. 173 (1935), 245–254.Google Scholar
- [G]S. Garoufalidis, Relations among 3-manifold invariants (University of Chicago Ph.D. thesis, 1992 ).Google Scholar
- [GJ]J. Glimm, A. Jaffe, Quantum Physics. A functional integral point of view., Sec-ond edition, Springer-Verlag, New York-Berlin, 1987.Google Scholar
- [GM]R. Gompf, R. Mrowka, Irreducible four-manifolds need not be complex (preprint, 1991 ).Google Scholar
- [H]N. Hitchin, Flat connections and geometric quantization, Commun. Math. Phys. 131 (1990), 347–380.MathSciNetADSMATHCrossRefGoogle Scholar
- [J]L. C. Jeffery, On some aspects of Chern-Simons gauge theory (Oxford Univ. D.Phil. thesis, 1991 ).Google Scholar
- [K]L. H. Kauffman, Knots and Physics, World Scientific, 1991.MATHGoogle Scholar
- [KM]V. G. Kac, M. Wakimoto, Adv. Math. 70 (1988), 156.MathSciNetMATHCrossRefGoogle Scholar
- [M]W. Miller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. Math. 28 (1978), 233–305.CrossRefGoogle Scholar
- [Q1]F. Quinn, Lectures on axiomatic topological quantum field theory (preprint, 1992 ).Google Scholar
- [Q2]F Quinn, Topological foundations of topological quantum field theory (preprint, 1991).Google Scholar
- [R]K. Reidemeister, Homotopieringe und Linsenrdume, Hamburger Abhandl 11 (1935), 102–109.MATHCrossRefGoogle Scholar
- [RS]D. B. Ray, L M. Singer, R-torsion and the laplacian on Riemannian manifolds, Adv. Math. 7 (1971), 145–210.MathSciNetMATHCrossRefGoogle Scholar
- [RSW]T. R. Ramadas, L M. Singer, J. Weitsman, Some comments on Chern-Simons, gauge theory, Commun. Math. Phys. 126 (1989), 409.MathSciNetADSMATHCrossRefGoogle Scholar
- [RT]N. Y. Reshetikhin, V. G. Turaev, Ribbon graphs and their invariants derived, from quantum groups, Commun. Math. Phys. 127 (1990), 1–26.MathSciNetADSMATHCrossRefGoogle Scholar
- [S]G. Segal, The definition of conformal field theory (preprint).Google Scholar
- [Sp]E. H. Spanier, Algebraic Topology, Springer-Verlag, New York, 1981.CrossRefGoogle Scholar
- [Wl]E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989), 351–399MathSciNetADSMATHCrossRefGoogle Scholar
- [W2]E. Witten, Topological sigma models, Commun. Math. Phys. 118 (1988), 411MathSciNetADSMATHCrossRefGoogle Scholar
- [Wa]K. Walker, On Witten’s 3-manifold invariants (preprint, 1991 )Google Scholar
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