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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 054, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.054
(Mi sigma1949)
 

This article is cited in 2 scientific papers (total in 2 papers)

Moduli Space for Kink Collisions with Moving Center of Mass

Christoph Adama, Chris Halcrowb, Katarzyna Olesc, Tomasz Romanczukiewiczc, Andrzej Wereszczyńskic

a Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago 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
References:
Abstract: 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.
Keywords: topological solitons, collective coordinates method, moduli space.
Funding agency Grant number
Ministerio de Educación, Cultura y Deporte, Spain PID2020-119632GB-I00
The Spanish Consolider-Ingenio 2010 Programme CPAN CSD2007-00042
Xunta de Galicia INCITE09.296.035PR
European Regional Development Fund
The authors acknowledge financial support from the Ministry of Education, Culture, and Sports, Spain (Grant No. PID2020-119632GB-I00), the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042), the Xunta de Galicia (Grant No. INCITE09.296.035PR and Centro singular de investigaci´on de Galicia accreditation 2019-2022), and the European Union ERDF. C.H. is supported by the Carl Trygger Foundation through the grant CTS 20:25. K.O., T.R., and A.W. were supported by the Polish National Science Centre (Grant No. NCN 2019/35/B/ST2/00059).
Received: April 20, 2023; in final form July 26, 2023; Published online August 2, 2023
Document Type: Article
MSC: 35C08, 35Q51
Language: English
Citation: Christoph Adam, Chris Halcrow, Katarzyna Oles, Tomasz Romanczukiewicz, Andrzej Wereszczyński, “Moduli Space for Kink Collisions with Moving Center of Mass”, SIGMA, 19 (2023), 054, 18 pp.
Citation in format AMSBIB
\Bibitem{AdaHalOle23}
\by Christoph~Adam, Chris~Halcrow, Katarzyna~Oles, Tomasz~Romanczukiewicz, Andrzej~Wereszczy{\'n}ski
\paper Moduli Space for Kink Collisions with Moving Center of Mass
\jour SIGMA
\yr 2023
\vol 19
\papernumber 054
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma1949}
\crossref{https://doi.org/10.3842/SIGMA.2023.054}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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