This article is cited in 2 papers

Example of a self-localizing nonlinear relativistic field

A. S. Davydov, N. I. Kislukha


Abstract: The real scalar relativistic field with self-interaction $(\lambda/4)\psi^4$ in the Lagrangian is studied. An exact solution is obtained for the one- and three-dimensional cases. It is shown that in the one-dimensional case the field is localized in a certain region whose size varies in accordance with a Lorentz transformation. The energy and momentum of the field are inversely proportional to the coupling constant, and they are related by the same relativistic equation as for a particle with a certain internal energy. In the three-dimensional case the field is localized only in one dimension.

Received: 14.08.1972

 English version: Theoretical and Mathematical Physics, 1973, 16:1, 702–705