The Rest-Frame Instant Form and Dirac Observables for the Open Nambu String

TL;DR

This paper develops a rest-frame instant form of the open Nambu string, describing it through a non-local canonical center of mass and gauge-invariant Dirac observables, with implications for canonical quantization.

Contribution

It introduces a novel rest-frame instant form for the open Nambu string, utilizing Wigner-covariant variables and Frenet-Serret methods to identify Dirac observables.

Findings

Decomposition into center of mass and relative variables

Construction of gauge-invariant Dirac observables

Discussion on canonical quantization approaches

Abstract

The rest-frame instant form of the positive-energy part of the open Nambu string is developed. The string is described as a decoupled non-local canonical non-covariant Newton-Wigner center of mass plus a canonical basis of Wigner-covariant relative variables living in the Wigner 3-spaces. The center of mass carries a realization of the Poincare' algebra depending upon the invariant mass and the rest-spin of the string, functions of the relative variables. A canonical basis of gauge invariant Dirac observables is built with Frenet-Serret geometrical methods. Some comments on canonical quantization are made.