A differential equation is proposed to describe the evolution of a screw dislocation in a continuous medium under an externally applied displacement field. The derivation is based on the conservation of energy and momentum and the neglect of radiation reaction and renormalizability: The equation of motion must be such that it allows for a renormalization of the infinite self-energy and momentum of the infinitely thin dislocation. The extent to which the result might hold for general dislocation loops is discussed.

• Received 7 November 1984

DOI:https://doi.org/10.1103/PhysRevLett.54.14