Generalization of the relativistic string model in the geometrical approach

✍ Scribed by B. M. Barbashov; V. V. Nesterenko; A. M. Chervjakov

• Publisher: Springer
• Year: 1979
• Tongue: English
• Weight: 237 KB
• Volume: 3
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00397208

✦ Synopsis

We present a model of a one-dimensional extended relativistic object, whose motion is defined by the requirement that its time track in Minkowski space is a surface of the constant mean curvature H. The world surface of the relativistic string is a particular case of such surfaces, namely, a minimal surface with H --0. By differential-geometry methods the theory of the proposed object moving in three-dimensional space-time is reduced to one nonhnear equation B~r -~P~a = Hsh~. In the theory under consideration, there naturally arises the pair of Lax's operators needed to solve this nonlinear equation by the inverse scattering method.