Quantization of a self-interacting maximally charged string

TL;DR

This paper explores the quantization of a self-interacting, maximally charged string, revealing a well-defined ground state and quantized energy levels of Planck mass order, extending previous black hole models to continuous matter.

Contribution

It introduces a quantization framework for a maximally charged matter string, including Hamiltonian construction and gauge fixing, generalizing black hole results to continuous matter distributions.

Findings

System has a well-defined ground state.

Energy level spacing is of order the Planck mass.

Extends black hole quantization results to continuous matter.

Abstract

We discuss the quantization of a self-interacting string consisting of maximally charged matter. We construct the Hamiltonian in the non-relativistic limit by expanding around a static solution of the Einstein-Maxwell field equations. Conformal symmetry is broken on the worldsheet, but a subgroup of the conformal group acts as the gauge group of the theory. Thus, the Faddeev-Popov quantization procedure of fixing the gauge is applicable. We calculate the Hamiltonian and show that, if properly quantized, the system possesses a well-defined ground state and the spacing of its energy levels is of order the Planck mass. This generalizes earlier results on a system of maximally charged black holes to the case of continuous matter distributions.