Towards Relativistic Skyrmions

TL;DR

This paper advances the Skyrme model by developing a relativistic framework for baryons, including a new gamma matrix representation and methods to compute form factors at arbitrary momenta.

Contribution

It introduces a novel relativistic wavefunction representation and gamma matrix formalism for baryons in the Skyrme model, enabling calculations at non-static momenta.

Findings

Derived a Dirac equation in the soliton collective space.

Showed how to compute vector current vacuum expectation values.

Demonstrated calculation of elastic form factors at arbitrary momenta.

Abstract

We revisit baryons in the Skyrme model. Starting from static baryons in the helicity eigenstates, we generalize their wavefunctions to the non-static and relativistic regime. A new representation for gamma matrices in the soliton collective space is constructed and the corresponding Dirac equation is obtained. As an example, we draw consideration on how to apply this new representation on the calculus of vector current vacuum expectation values for baryon states of spin and isospin half and arbitrary momenta and we show how elastic form factors can be derived.