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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.38 no.3 (2011), pp. 293-302
Quantum Equations of Motion in BF Theory with Sources
A. Alekseev1, N. Ilieva2
1Section de mathématiques, Université de Genéve, 1211 Genéve 4, Switzerland
2Institute of Nuclear Research and Nuclear Energy, Bulg. Acad. Sci., Sofia 1784, Bulgaria
go back1Section de mathématiques, Université de Genéve, 1211 Genéve 4, Switzerland
2Institute of Nuclear Research and Nuclear Energy, Bulg. Acad. Sci., Sofia 1784, Bulgaria
Abstract. The 2-dimensional BF theory is both a gauge theory and a topological Poisson σ-model corresponding to a linear Poisson bracket. In [1], Torossian discovered a connection which governs correlation functions of the BF theory with sources for the B-field. This connection is flat, and it is a close relative of the KZ connection in the WZW model. In this paper, we show that flatness of the Torossian connection follows from (properly regularized) quantum equations of motion of the BF theory.