Imaginary Sources: Completeness Conjecture and Charges

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.