Abstract
This paper concerns the quantization of massless quantum electrodynamics on a general two-dimensional Riemannian manifold (QED2). The central result is the derivation of the propagators and vertex correlation functions at the lowest order on any closed and orientable Riemann surface. This also allows the perturbative treatment of QED2 in the case of non-trivially curved spacetimes and the explicit calculation of the physical observables at any order. Moreover, the perturbative approach described in this paper can also be applied to string theories. To this purpose, two models are presented describing possible interactions between Abelian gauge fields and string theory.
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