Scaling Identities for Solitons beyond Derrick's Theorem

TL;DR

This paper introduces new integral identities for topological solitons in classical field theories, derived from stress tensor conservation and rescaling arguments, refining Derrick's theorem.

Contribution

It presents novel integral identities for solitons, extending Derrick's theorem through stress tensor considerations and independent rescaling methods.

Findings

Derived new integral identities for solitons

Refined Derrick's theorem with stress tensor conservation

Applicable to various classical field theories

Abstract

New integral identities satisfied by topological solitons in a range of classical field theories are presented. They are derived by considering independent length rescalings in orthogonal directions, or equivalently, from the conservation of the stress tensor. These identities are refinements of Derrick's theorem.