Abstract
A systematic approach to 2-dimensional quantum field theories with to pological terms in the action is developed using as a mathematical tool the Deligne cohomology. As an application,it is shown how to bosonize the action of free fermions of arbitrary spin on a Riemann surface and how to find the spectrum of the Wess-Zumino-Witten sigma models without recurrence to modular invariance.
Extended version of lectures delivered at the Summer School on Nonperturbative Quantum Field Theory, Cargese 1987.
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References
P.A.M. Dirac, Proc. R. Soc. London A133,60 (1931).
D.J. Simms, N.M. Woodhouse,LectureNotesinPhysics,Vol.53,Springer(1976).
E. Witten, Commun.Math.Phys. 92, 455 (1984).
L. Alvarez-Gaumé, J.-B. Bost, G. Moore, P. Nelson,C Vafa,Phys.Lett.B178,105 (1986).
D. Gepner,E. Witten,Nucl.Phys. B278,493 (1986).
P.A.M Dirac The principles of quantum mechanics,4th edition Oxford University Press(1958)
R.P. Feynman,A.R. Hibbs,Quantum mechanics and path integrals,Mc.Graw-Hill.
T.T. Wu,C.N. Yang,Phys. Rev. D14, 437 (1976).
Y. Aharonov,D. Bohm, Phys.Rev.115, 485 (1959).
A.Kirillov,Elements de la theorie des representations,Editions Mir(1974).
B.Kostant,in Lecture Notes in Math.,Vol.170,pp.87-208,Springer
R.Godement,To pologie algebrique et theorie des faisceaux,Hermann(1964).
C.G. Callan,R.F. Dashen,D.J. Gross,Phys.Let. 63B,334 (1976).
R. Jackiw,C. Rebbi, Phys. Rev. Lett. 37, 172 (1976).
T.R. Ramadas,Commun. Math.Phys. 93, 355 (1984 ).
H.Esnault,E.Viehweg,Deligne-Beilinsoncohomology,publicationofMax-Planck-InstitutfurMathematik,Bonn.
O. Alvarez, Commun.Math.Phys. 100, 279 (1985).
R. Hamilton, Bull. Am.Math.Soc. 7, 65 (1982).
D. Friedan,E. Martinec,S. Shenker, Nucl.Phys. B271, 93 (1986).
L. Alvarez-Gaumé, J.B. Bost, G. Moore,P. Nelson,C. Vafa, BOzonization on higher genus Riemann surfaces Harvard-CERN preprint
V.G. Knizhnik,A.B. Zamolodchikov, Nucl.Phys. B247,83 (1984).
A. Pressley,G. Segal, Loopgroups,ClarendonPress (1986).
V.G.Kac,InfinitedimensionalLiealgebras,CambridgeUniversityPress(1985).
.V.G.Kac,D.H.Peterson,inArithmeticsandgeometry,Vol.2,pp.141-166,Birkhauser(1983).
G.Felder,K.Gawedzki,A.Kupiainen,ThespectrumofWess-Zumino-Wittenmodels,IHESpreprint.
D. Gepner, Nucl.Physics. B287,111 (1987).
A. Cappeli,C. Itzykson, J.B. Zuber, Nucl.Phys.B280 [FS 18],445 (1987) and the A-D-E classification of minimal and A1(1) conformal invariant theories to appear in Commun. Math. Phys.
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© 1988 Plenum Press, New York
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Gawędzki, K. (1988). Topological Actions in Two-Dimensional Quantum Field Thories. In: ’t Hooft, G., Jaffe, A., Mack, G., Mitter, P.K., Stora, R. (eds) Nonperturbative Quantum Field Theory. Nato Science Series B:, vol 185. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0729-7_5
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DOI: https://doi.org/10.1007/978-1-4613-0729-7_5
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