A Solution to Non-Linear Equations of Motion of Nambu-Goto String

TL;DR

This paper presents a method to solve the non-linear equations of motion for the Nambu-Goto string using ultradistributions, introduces the concept of anti-string, and computes the string field propagator and its convolution.

Contribution

It introduces ultradistributions of exponential type for string description, proves the string field as a superposition of compact support ultradistributions, and defines the notion of anti-string.

Findings

Solved the non-linear equations of motion for the Nambu-Goto string.

Proved the string field can be expressed as a superposition of ultradistributions.

Calculated the propagator and its convolution for the string field.

Abstract

In this paper we solve the non-linear Lagrange's equations for the Nambu-Goto closed bosonic string. We show that Ultradistributions of Exponential Type (UET) are appropriate for the description in a consistent way string and string field theories. We also prove that the string field is a linear superposition of UET of compact support (CUET), and give the notion of anti-string. We evaluate the propagator for the string field, and calculate the convolution of two of them.