2020/08/31 by N. S. Manton, K. Oleś, T. Romańczukiewicz +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.103.025024
published as Phys. Rev. D 103, 025024 (2021) · presentation improved, new plots added
arxiv created 2020/11/18 · arxiv updated 2021/02/03
Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in ϕ4 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 ϕ4 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.