  While in string theory the subject of sources in imaginary time has received
some attention, we demonstrate the power of imaginary sources by proving that
they constitute in several field theories a complete basis for all smooth and
time dependent source free solutions. These proofs promote the study of
imaginary sources to a new and crucial viewpoint for understanding time
dependent backgrounds. From our field theory examples we further propose a
completeness conjecture that every regular solution to a field equation of
motion has a corresponding imaginary source configuration. We define charges
for spacelike sources and show their compatibility with the usual charge
definition for timelike sources. Many new non-singular time dependent field
theory solutions are discussed, including Wick rotations of abelian instantons
which demonstrate a close relationship between electric-magnetic duals and
analytic continuation.
