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Nonlinearity, Geometry and Field Theory Solitons

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Emerging Frontiers in Nonlinear Science

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 32))

Abstract

Topological solitons occur in many types of nonlinear field theory. Their motion and interactions can be simulated classically, and can be well approximated by a finite-dimensional dynamics on a moduli space of collective coordinates. Interesting phenomena related to the curvature and topology of moduli spaces are illustrated here through the examples of vortices, sigma model lumps, and monopoles. Collective coordinate dynamics can be quantized, and it is shown how quantized Skyrmion dynamics is used to understand aspects of nuclear physics. A novel model for nuclear fusion, based on wormhole geometry, is also proposed.

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Acknowledgements

The half-wormhole model for Oxygen-16 interacting with an alpha particle was developed following a talk by Takashi Nakatsukasa and a related question concerning Newton’s cradle by Panagiota Papakonstantinou, at the 1st APCPT-TRIUMF Joint Workshop, Pohang, Korea, 2018. I also thank J. Martin Speight and Maciej Dunajski for helpful discussions. This work has been partially supported by STFC consolidated grant ST/P000681/1.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    Nicholas S. Manton

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  1. Nicholas S. Manton
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Correspondence to Nicholas S. Manton .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    Panayotis G. Kevrekidis

  2. Grupo de Fisica No Lineal, Departamento de Fisica Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Seville, Spain

    Jesús Cuevas-Maraver

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    Avadh Saxena

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Manton, N.S. (2020). Nonlinearity, Geometry and Field Theory Solitons. In: Kevrekidis, P., Cuevas-Maraver, J., Saxena, A. (eds) Emerging Frontiers in Nonlinear Science. Nonlinear Systems and Complexity, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-44992-6_9

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