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The finite-volume QED$_{1+1}$ is formulated in terms of Dirac variables by anexplicit solution of the Gauss constraint with possible nontrivial boundaryconditions taken into account. The intrinsic nontrivial topology of the gaugegroup is thus revealed together with its zero-mode residual dynamics.Topologically nontrivial gauge transformations generate collective excitationsof the gauge field above Coleman's ground state, that are completely decoupledfrom local dynamics, the latter being equivalent to a free massive scalar fieldtheory.Comment: 13 pages, LaTe

DIRAC VARIABLES AND ZERO MODES OF GAUSS CONSTRAINT IN FINITE-VOLUME TWO-DIMENSIONAL QED