Quantum Nucleation of Vortex String Loops

TL;DR

This paper studies the quantum nucleation process of vortex string loops in a relativistic scalar field theory, calculating nucleation rates and loop sizes, and explores related phenomena in Maxwell-Higgs systems with potential physical implications.

Contribution

It introduces a method to compute quantum nucleation rates of vortex loops using Euclidean path integrals and analyzes the dynamics of induced currents within vortex loops.

Findings

Nucleation rate and critical vortex loop size are estimated.

Induced currents inside vortex loops oppose initial currents, reducing the initial current.

Discussion of similar processes in Maxwell-Higgs systems and their implications.

Abstract

We investigate quantum nucleation of vortex string loops in the relativistic quantum field theory of a complex scalar field by using the Euclidean path integral. Our initial metastable homogeneous field dominated by the $O(3)$ symmetric bounce solution. The nucleation rate and the critical vortex loop size are obtained approximately. Gradually the initial current will be reduced to zero as the induced current inside vortex loops is opposite to the initial current. We also discuss a similar process in Maxwell-Higgs systems and possible physical implications.