Kink Moduli Spaces -- Collective Coordinates Reconsidered

Abstract

Moduli spaces - finite-dimensional, collective coordinate manifolds - for kinks and antikinks in ${\varphi }^4$ 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 ${\varphi }^4$ 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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Cited by in corpus (32)

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• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Deformations of Kink Tails
• Resonance structures in kink-antikink collisions in a deformed sine-Gordon model
• Resonance mediated by fermions in kink-antikink collisions
• Inclusion of radiation in the CCM approach of the ${\varphi }^4$ model
• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Collective coordinates for the hybrid model
• Fermions on wobbling kinks: normal versus quasinormal modes
• Scattering of compact kinks
• Moving Kinks and Their Wave Packets
• Constrained instantons and kink-antikink collisions
• Highly-enhanced propagation of long-range kinks in heterogeneous media
• Connections between kinks with different asymptotics
• Compact kink and its interaction with compact oscillons
• Linearly stable and unstable complex soliton solutions with real energies in the Bullough-Dodd model
• Moduli space with a boundary
• Moduli spaces for PT-regularized solitons
• Kink-antikink collisions in hyper-massive models
• Solving the Spectral Problem via the Periodic Boundary Approximation in ${\varphi }^6$ Theory
• Moduli Space for Kink Collisions with Moving Center of Mass
• The impact of thermal noise on kink propagation through a heterogeneous system
• Compact kinks in a modified Christ-Lee model
• Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints
• Collective coordinate descriptions of a kink in a driven-damped ${\varphi }^4$ model