  We consider the Dirichlet to Neumann operator for abelian Yang- Mills
boundary conditions. We treat the case for space-time manifolds with general
smooth boundary components. The aim is constructing a complex structure for the
symplectic space of boundary conditions of Euler-Lagrange solutions modulo
gauge. Thus we prepare a suitable scenario for geometric quantization of
abelian gauge fields following a symplectic reduction procedure in a Lagrangian
setting.
