The Rotation and Shear of a String

TL;DR

This paper explores the concepts of rotation and shear in strings through an analogy with point particles, identifying optimal vector fields via stress conservation and examining related equations and membrane-fluid relationships.

Contribution

It introduces a novel approach to analyze string rotation and shear by using stress conservation to identify key vector fields and derives related equations.

Findings

Optimal vector field is a non-unit accelerating field in x

Derived an equation for the spacetime derivative of the Lagrangian

Examined the relationship between membranes and fluids

Abstract

Whether a string has rotation and shear can be investigated by an anology with the point particle. Rotation and shear involve first covariant spacetime derivatives of a vector field and, because the metric stress tensor for both the point particle and the string have no such derivatives, the best vector fields can be identified by requiring the conservation of the metric stress. It is found that the best vector field is a non-unit accelerating field in x, rather than a unit non-accelerating vector involving the momenta; it is also found that there is an equation obeyed by the spacetime derivative of the Lagrangian. The relationship between membranes and fluids is looked at.