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arXiv · 2008.01026

Kink Moduli Spaces -- Collective Coordinates Reconsidered

N. S. Manton·K. Oleś·T. Romańczukiewicz·A. Wereszczyński
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Abstract

Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in $\phi^4$ theory and sine-Gordon theory are reconsidered. The field theory Lagrangian restricted to moduli space defines a reduced Lagrangian, combining a potential with a kinetic term that can be interpreted as a Riemannian metric on moduli space. Moduli spaces should be metrically complete, or have an infinite potential on their boundary. Examples are constructed for both kink-antikink and kink-antikink-kink configurations. The naive position coordinates of the kinks and antikinks sometimes need to be extended from real to imaginary values, although the field remains real. The previously discussed null-vector problem for the shape modes of $\phi^4$ kinks is resolved by a better coordinate choice. In sine-Gordon theory, moduli spaces can be constructed using exact solutions at the critical energy separating scattering and breather (or wobble) solutions; here, energy conservation relates the metric and potential. The reduced dynamics on these moduli spaces accurately reproduces properties of the exact solutions over a range of energies.

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N. S. Manton, K. Oleś, T. Romańczukiewicz, A. Wereszczyński. 2020-08-03. Kink Moduli Spaces -- Collective Coordinates Reconsidered. https://doi.org/10.1103/physrevd.103.025024

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