VORTEX DYNAMICS OF THE NONLINEAR-WAVE EQUATION

ψ is a complex scalar field defined on (2 + 1 - D)-dimensional Minkowski space. It satisfies the nonlinear wave equation (NLWE) □ψ-(1-|ψ|)ψ = 0 We study the solutions which contain time-like world lines of zeros, with winding numbers +1 or -1. We call these particle-like defects of the ψ field vortices. We formulate an asymptotic "particle + field" vortex dynamics which derives from the NLWE. It is analogous to particle + field electrodynamics in 2 + 1 - D. In particular, the winding number plays the role of charge, and gradients, of arg ψ play the role of the electromagnetic field. © 1990.