Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 054, 18 pages      arXiv:2304.07895
Contribution to the Special Issue on Topological Solitons as Particles

Moduli Space for Kink Collisions with Moving Center of Mass

Christoph Adam a, Chris Halcrow b, Katarzyna Oles c, Tomasz Romanczukiewicz c and Andrzej Wereszczynski c
a) Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782Santiago de Compostela, Spain
b) Department of Physics, KTH-Royal Institute of Technology, SE-10691 Stockholm, Sweden
c) Institute of Theoretical Physics, Jagiellonian University, Lojasiewicza 11, Kraków, Poland

Received April 20, 2023, in final form July 26, 2023; Published online August 02, 2023

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.

Key words: topological solitons; collective coordinates method; moduli space.

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