Second quantization of a covariant relativistic spacetime string in Steuckelberg-Horwitz-Piron theory

TL;DR

This paper develops a covariant quantum framework for a relativistic 4D spacetime string, utilizing solutions of the relativistic harmonic oscillator, and introduces a novel formalism for quantizing extended systems with derived spectra.

Contribution

It introduces a new formalism for quantizing a covariant relativistic spacetime string within the Stueckelberg-Horwitz-Piron theory, including the continuum limit and spectral analysis.

Findings

Derived mass and energy spectra for the string

Developed a new quantization approach for extended systems

Compared results with existing string models

Abstract

A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg (1941) [1], and further developed by Horwitz and Piron (1973) [2], and discussed at length in the book of Horwitz (2015) [3]. We describe the space-time string using the solutions of relativistic harmonic oscillator [4]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.