Stabilization of the Skyrmion by the Quantisation of Collective Vibrations and Rotations

Abstract

<p>The classical solitons of the minimal σ-model, the Skyrme model without the quartic term, are known to be unstable to scale variations (Derrick's theorem). Although it has been suggested that these solitons might be stabilized by quantum effects, this possibility has not been adequately investigated. Existing treatments lead to new instabilities due to the improper introduction and treatment of collective and intrinsic degrees of freedom.</p> <p>In this work, we detail the quantisation of collective vibrations and rotations of the Skyrmion in the Dirac formalism for constrained Hamiltonian systems in which we include intrinsic pion field fluctuations. We show that in the absence of the quartic term, the soliton, which disappears in the classical limit, is stabilized by quantum effects alone. The coupling between rotations, vibrations and the intrinsic pion field is found to play an important role in the stability of the soliton.</p> <p>We derive and solve the Skyrmion equation of motion which now includes quantum corrections leading to the stability of the soliton. The stable soliton is shown to possess a symmetry under scale transformations. In either limiting case of rotations or vibrations only, the soliton is shown to be unstable. On the other hand, the rotating vibrating Skyrmion is stable yet it has different properties in different quantum states, a desirable physical property exhibiting the fluid nature of the Skyrmion.</p> <p>Comparison with the static properties of baryons and the conventional Skyrme model shows that the qualitative agreement with experimental results is not significantly altered by the presence or absence of the quartic term.</p>