Free and Interacting 2-D Maxwell Field Theory on Conformally Flat Space Times

摘要

The free Maxwell field theory is quantized in the Lorentz gauge on a twodimensional manifold $M$ with conformally flat background metric. It is shownthat in this gauge the theory is equivalent, at least at the classical level,to a biharmonic version of the bosonic string theory. This equivalence isexploited in order to construct in details the propagator of the Maxwell fieldtheory on $M$. The expectation values of the Wilson loops are computed. Atrivial result is obtained confirming in the Lorentz gauge previouscalculations. Finally the interacting case is briefly discussed taking theSchwinger model as an example. The two and three point functions of theSchwinger model are explicitly derived at the lowest order on a Riemannsurface.