Decoupling of Translational and Rotational Modes for a Quantum Soliton

TL;DR

This paper derives and verifies integral relations for zero modes of solitons across various models, ensuring proper quantization and Hamiltonian formulation by decoupling translational and rotational motions.

Contribution

It introduces integral relations for zero modes that facilitate consistent quantization and decoupling of translational and rotational modes in soliton models.

Findings

Derived integral relations for zero modes in multiple soliton models.

Verified relations ensure correct kinetic and centrifugal terms in Hamiltonian.

Connected properties to virial relations for broader theoretical consistency.

Abstract

A set of integral relations for rotational and translational zero modes in the vicinity of the soliton solution are derived from the particle-like properties of the latter and verified for a number of models (solitons in 1+1-dimensions, skyrmeons in 2+1- and 3+1-dimensions, non-abelian monopoles). It is shown, that by consistent quantization within the framework of collective coordinates these relations ensure the correct diagonal expressions for the kinetic and centrifugal terms in the Hamiltonian in the lowest orders of the perturbation expansion. The connection between these properties and virial relations is also determined.