Quantum soliton scattering manifolds

Abstract

We consider the quantum multisoliton scattering problem. For BPS theories one truncates the full field theory to the moduli space, a finite dimensional manifold of energy minimising field configurations, and studies the quantum mechanical problem on this. Non-BPS theories -- the generic case -- have no such obvious truncation. We define a quantum soliton scattering manifold as a configuration space which satisfies asymptotic completeness and respects the underlying classical dynamics of slow moving solitons. Having done this, we present a new method to construct such manifolds. In the BPS case the dimension of the $n$-soliton moduli space ${\mathcal{M}}_n$ is $n$ multiplied by the dimension of ${\mathcal{M}}_1$. We show that this scaling is not necessarily valid for scattering manifolds in non-BPS theories, and argue that it is false for the Skyrme and baby-Skyrme models. In these models, we show that a relative phase difference can generate a relative size difference during a soliton collision. Asymptotically, these are zero and non-zero modes respectively and this new mechanism softens the dichotomy between such modes. Using this discovery, we then show that all previous truncations of the 2-Skyrmion configuration space are unsuitable for the quantum scattering problem as they have the wrong dimension. This gives credence to recent numerical work which suggests that the low-energy configuration space is 14-dimensional (rather than 12-dimensional, as previously thought). We suggest some ways to construct a suitable manifold for the 2-Skyrmion problem, and discuss applications of our new definition and construction for general soliton theories.

24 pages, 8 figures

References in corpus (9)

• Multisolitons in a Two-dimensional Skyrme Model
• Dynamics of Baby Skyrmions
• Skyrmions, Fullerenes and Rational Maps
• Non-Abelian Vortices of Higher Winding Numbers
• Skyrmions up to Baryon Number 108
• Vibrational modes of Skyrmions
• The Casimir energy of skyrmions in the 2+1-dimensional O(3)-model
• Roper resonances and quasi-normal modes of Skyrmions
• Kähler quantization of vortex moduli

Cited by in corpus (7)

• Two-Loop Scalar Kinks
• Spectral walls in multifield kink dynamics
• Kink-antikink collisions in a weakly interacting ${\varphi }^4$ model
• Baby Skyrmion crystals
• A consistent two-skyrmion configuration space from instantons
• An Alternative to Collective Coordinates
• Manipulation and trapping of magnetic skyrmions with domain walls in chiral magnetic thin films