Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-11-10
Class.Quant.Grav.10:1065-1082,1993
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, LMU-TPW 92-8, (plain TeX)
Scientific paper
10.1088/0264-9381/10/6/005
The free Maxwell field theory is quantized in the Lorentz gauge on a two dimensional manifold $M$ with conformally flat background metric. It is shown that in this gauge the theory is equivalent, at least at the classical level, to a biharmonic version of the bosonic string theory. This equivalence is exploited in order to construct in details the propagator of the Maxwell field theory on $M$. The expectation values of the Wilson loops are computed. A trivial result is obtained confirming in the Lorentz gauge previous calculations. Finally the interacting case is briefly discussed taking the Schwinger model as an example. The two and three point functions of the Schwinger model are explicitly derived at the lowest order on a Riemann surface.
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