Relativistic collective coordinate quantization of solitons: Spinning Skyrmion

Abstract

We develop a consistent relativistic generalization of collective coordinate quantization of field theory solitons. Our principle of introducing collective coordinates is that the equations of motion of the collective coordinates ensure those of the original field theory. We illustrate this principle with the quantization of spinning degrees of freedom of Skyrmion representing baryons. We calculate the leading relativistic corrections to the static properties of nucleons, and find that the corrections are non-negligible ones of 10% to 20%.

Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

“…Finally our method is general so that we can apply it to other BPS solitons such as domain walls, monopoles and instantons, or non-BPS solitons such as Skyrmions. In the same spirit, four derivative term in the form of the Skyrme term was obtained in the effective theory of non-Abelian domain walls [23], and four derivative terms for collective coordinates of a rotating Skyrmion were calculated [24].…”

“…More recently, the moduli space dynamics has been successfully applied even to 1/4 BPS composite solitons such as domain wall networks [21] and strings stretched between parallel domain walls [22]. Although there has been a lot of remarkable progress in study of the moduli space of BPS solitons, the analysis of their dynamics has been restricted to the leading order of the low-energy (small-velocity) limit, except for a few examples [23,24].…”

Kink interactions in the(1+1)-dimensionalφ6model

“…In this context, see also Refs. [26,27], which develop a relativistic generalization of the collective coordinate method and perform the quantization of the rotational motion of the skyrmion. A general discussion of the collective coordinate method involving the discrete (vibrational) mode of a kink is given in the review [2].…”

On the spin excitation energy of the nucleon in the Skyrme model

“…Here we shall argue that the trustworthy value is M s ≈ 16 MeV, and that the much higher result from the rigid rotor quantization of the Delta resonance cannot be trusted. Our argument (but see also [26], [28]) is that the rigid rotor approximation is valid only in a non-relativistic regime. By re-interpreting the rotational excitations in the fit to the Delta as classical rotations we shall find, however, that these rotations are highly relativistic and the application of the rigid rotor approximation is, therefore, not justified.…”