Structure of singularities on the world sheets of relativistic strings

TL;DR

This paper investigates the topologically stable singularities on the world sheets of relativistic strings in 3 and 4-dimensional Minkowski space, analyzing their structure, normal forms, and conservation laws.

Contribution

It introduces a detailed analysis of singularities on relativistic strings, including their normal forms and a conserved topological charge, expanding understanding of string world sheet topology.

Findings

Relativistic strings have topologically stable singular points.

Singularities possess a conserved topological charge.

The paper describes normal forms of these singularities.

Abstract

We show that relativistic strings of open and closed types in Minkowski space-time of dimension 3 and 4 have topologically stable singular points. This paper describes the structure of singularities, derives their normal forms, and introduces a local characteristic of singularity (topological charge), possessing a global law of conservation. Two other types of solutions (breaking and exotic strings) are also considered, which have singularities at arbitrary value of dimension.