Relativistic Moduli Space for Kink Collisions

Abstract

The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections {\it perturbatively} in kink scattering. It gives an excellent description of kink-antikink collisions in ${\varphi }^4$ field theory already at first order, and at higher order, reproduces the fractal structure in the formation of the final state with an error of only $4\%$.

v4: Minor revisions. This version accepted for publication in Physical Review D

References in corpus (10)

• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Spectral Walls in Soliton Collisions
• Collective coordinate model of kink-antikink collisions in ${\varphi }^4$ theory
• Scattering between wobbling kinks
• Kink Moduli Spaces -- Collective Coordinates Reconsidered
• Spectral walls in multifield kink dynamics
• Fractal structure of the soliton scattering for the graphene superlattice equation
• Wobbling double sine-Gordon kinks
• Sphalerons and resonance phenomenon in kink-antikink collisions
• Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model

Cited by in corpus (17)

• Multikink scattering in the ${\varphi }^6$ model revisited
• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Inclusion of radiation in the CCM approach of the ${\varphi }^4$ model
• Spectral walls in antikink-kink scattering in the ${\varphi }^6$ model
• Resonance structures in kink-antikink scattering in a quantum vacuum
• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Scattering of kinks in the $B{\phi }^4$ model
• Scattering of compact kinks
• Constrained instantons and kink-antikink collisions
• Compact kink and its interaction with compact oscillons
• Wobbling kinks and shape mode interactions in a coupled two-component ${\varphi }^4$ theory
• Moduli space with a boundary
• Moduli Space for Kink Collisions with Moving Center of Mass
• Kink-antikink collisions in hyper-massive models
• Scattering between orthogonally wobbling kinks
• Collective coordinate descriptions of a kink in a driven-damped ${\varphi }^4$ model
• Negative radiation pressure in the abelian Higgs model