Two-dimensional electrodynamics and the global structure of space

Two-dimensional electrodynamics based on the spacetime S1(X)R is formulated using Fourier series and Dirac's constraint theory. The role of the background electric field F as a dynamical variable is established. The authors show that the background field is unstable against a class of charged pair creation processes involving the global topology of S1 provided mod F mod >1/2e, where e is the unit of electric charge. The results do not require any discussion of the Coulomb Green function or of the role of charges on spatial boundaries.