Moduli Space for Kink Collisions with Moving Center of Mass

• Published in: Symmetry, integrability and geometry, methods and applications Vol. 19
• Main Authors: Adam, Christoph, Halcrow, Chris, Oles, Katarzyna, Romanczukiewicz, Tomasz, Wereszczynski, Andrzej
• Format: Journal Article
• Language: English
• Published: 01-01-2023
• Subjects: collective coordinates method; moduli space; topological solitons
• ISSN: 1815-0659; 1815-0659
• DOI: 10.3842/SIGMA.2023.054

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.