Closed Strings with Low Harmonics and Kinks

TL;DR

This paper introduces formulas and parametrizations for closed relativistic strings with low harmonics, including methods to construct strings with kinks and analyze their self-intersections, relevant for cosmic string models.

Contribution

It provides new parametrizations for adding second- and third-harmonic waves to fundamental string waves, and discusses a systematic way to represent kinks from self-intersection and intercommutation.

Findings

Formulas for low-harmonic closed strings are derived.

A product representation for string Fourier series is developed.

Procedures for representing kinks from self-intersection are outlined.

Abstract

Low-harmonic formulas for closed relativistic strings are given. General parametrizations are presented for the addition of second- and third-harmonic waves to the fundamental wave. The method of determination of the parametrizations is based upon a product representation found for the finite Fourier series of string motion in which the constraints are automatically satisfied. The construction of strings with kinks is discussed, including examples. A procedure is laid out for the representation of kinks that arise from self-intersection, and subsequent intercommutation, for harmonically parametrized cosmic strings.