  The finite-volume QED$_{1+1}$ is formulated in terms of Dirac variables by an
explicit solution of the Gauss constraint with possible nontrivial boundary
conditions taken into account. The intrinsic nontrivial topology of the gauge
group is thus revealed together with its zero-mode residual dynamics.
Topologically nontrivial gauge transformations generate collective excitations
of the gauge field above Coleman's ground state, that are completely decoupled
from local dynamics, the latter being equivalent to a free massive scalar field
theory.
