The Hamilton-Jacobi Equations for Strings and p-Branes

TL;DR

This paper derives the Hamilton-Jacobi equations for classical bosonic strings and p-branes, presenting local field equations that generalize classical dynamics without linear terms.

Contribution

It provides a simple derivation of Hamilton-Jacobi equations for strings and p-branes, introducing nonlinear local field equations that extend classical descriptions.

Findings

Derivation of Hamilton-Jacobi equations for strings and p-branes

Introduction of nonlinear local field equations

Equivalence to classical Hamilton-Jacobi in the classical limit

Abstract

Simple derivation of the Hamilton-Jacobi equation for bosonic strings and p-branes is given. The motion of classical strings and p-branes is described by two and p+1 local fields, respectively. A variety of local field equations which reduce to the Hamilton-Jacobi equation in the classical limit are given. They are essentially nonlinear, having no linear term.