Covariant Quantization of the Skyrmion

TL;DR

This paper develops a Lorentz covariant quantization method for skyrmions, deriving their spin and isospin degrees of freedom through Green functions and S-matrix formalism, which naturally incorporates different quantization schemes.

Contribution

It introduces a covariant quantization framework for skyrmions that unifies the treatment of their internal degrees of freedom and includes novel topological considerations.

Findings

Derives a covariant two-point function for skyrmions.

Reproduces the non-relativistic collective coordinate method as a limit.

Provides a natural way to obtain boson and fermion quantizations of the skyrmion.

Abstract

We obtain the internal degrees of freedom of the skyrmion (spin and isospin) within a manifestly Lorentz covariant quantization framework based on defining Green functions for skyrmions and then, the S-matrix via LSZ reduction. Our method follows Frohlich and Marchetti's definition of Euclidean soliton Green functions, supplemented with a careful treatment of the boundary conditions around the singularities. The covariant two-point function obtained propagates a tower of spin equal to isospin particles. Our treatment contains the usual method of collective coordinates, as a non-relativistic limit and, because of the new topology introduced, it leads, in a natural way, to the inequivalent (boson/fermion) quantizations of the SU(2) skyrmion.