Baby Skyrmions stabilized by canonical quantization

Abstract

We analyse the effect of the canonical quantization of the rotational mode of the O(3) σ-model which includes the Skyrme term. Numerical evidence is presented that the quantum correction to the mass of the rotationally-invariant charge n = 1, 2 configurations may stabilize the solution even in the limit of vanishing potential. The corresponding range of values of the parameters is discussed.

Collective coordinate quantization and spin statistics of the solitons in theCPNSkyrme-Faddeev model

“…For this reason we shall begin presenting analysis of the CP 1 baby skyrmions. The full canonical quantization of the model has already been studied [15], however, in absence of the Hopf term. We consider the collective coordinate quantization taking into account the Hopf term and discuss the spin of the baby skyrmions.…”

“…In such a case the numerical analysis is required in order to compute the quantum corrections. The numerical analysis for the classical solutions of (15) has been extensively studied in [7]. Here we shall employ the potential…”

“…The research of quantum properties of solitons is important not only from a mathematical but also from a phenomenological point of view (mass spectrum, spin-statistics relation). There are many attempts to find a quantum theory of skyrmions in 2+1 dimensional CP N model, including full canonical quantization scheme [8][9][10][11][12][13][14][15]. In this paper we shall generalize a scheme of quantization, usually discussed for N = 1, to an arbitrary value N .…”

“…A similar approach has been applied to the * Electronic address: amalyamary@gmail.com † Electronic address: pawel.klimas@ufsc.br ‡ Electronic address: sawado@ph.noda.tus.ac.jp Skyrme-Faddeev Hopfions [21,22]. An alternative approach based on a canonical quantization method has been already examined for the baby Skyrme model [15] and the Skyrme-Faddeev Hopfions [23].…”

“…It is much easier to find a suitable parametrization consistent for the new condition. Thus the standard method for the quantization developed in [15][16][17][18][19][20][21][22][23] can be directly applied to the Hermitian variable X, than the principal variable Ψ itself. 1 .…”