NONLINEARITY, THE CHOICE OF GREEN-FUNCTION AND SELF-REGULARIZATION IN QUANTUM VORTEX DYNAMICS

The non-linearity of vortex dynamics implies a relation between asymptotic behaviour or boundary conditions and the dynamics of the sources (vortices or strings) and a regularized self-interaction. Therefore in the linearized approximation to vortex dynamics the Green function is not arbitrary, and the cutoff parameter used to regularize self interactions is completely determined in terms of parameters of the field theoretical model. It is shown that linearized vortex dynamics should be. a Fokker-type, action-at-a-distance theory. Consequently, the correct Green function is the time-symmetric one. These results are applied to three vortex configurations, where general existence conditions and a formula for the cutoff parameter is deduced. The bound state of antiparallel global cosmic strings is also discussed. Applications to cosmology and gravitation are briefly discussed.