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

Special Issue on Topological Solitons as Particles

The Guest Editors for this special issue are

Bernd J. Schroers (University of Edinburgh, UK)
Martin Speight (University of Leeds, UK)
Paul Sutcliffe (Durham University, UK)

This special issue of SIGMA celebrates the birthdays of two scientists who contributed perhaps more than anyone else to the exploration and development of the idea that topological solitons can be used to model physical particles. Nicholas Manton, who turned 70 in 2022, advanced the understanding of the structure and dynamics of a wide range of topological solitons in his research, and co-authored an authoritative textbook on the subject. Tony Skyrme, who would have turned 100 in 2022, was a widely respected nuclear physicist who invented the first topological soliton model of physical particles – the Skyrme model of nuclei. Their research intersects in the Skyrme model which, however, plays rather different and in a certain sense opposite roles in their respective outputs: Tony Skyrme is famous for his model even though it is only a small part of his oeuvre, and one which was never accepted by his own research community as a serious contender for a fundamental theory of nuclear matter. On the other hand, Nick Manton's best known results – the discovery of sphalerons, and the proposal of the geodesic approximation to soliton dynamics – are not directly linked to the Skyrme model, and yet it is perhaps the most persistent theme in and driver of his research.

It is fitting, even if entirely coincidental, that half of the contributions to his volume refer to the Skyrme model in their titles. However, all the contributions show the influence of Nick Manton's research and reflect his style of work, in particular the consistent use of geometrical, coordinate-independent concepts for addressing questions of physical interest in essentially nonlinear mathematical models. The contributors exemplify the breadth and versatility of the mathematicians and physicists working on topological solitons. Research in this area has created a rather unique research community which brings into dialogue geometers, physicists and experts in the numerical solution of nonlinear partial differential equations. This, too, is tribute to Nick Manton's way of thinking and his unique ability to communicate and collaborate with researchers in any of these specialities.

For us, as Nick Manton's former PhD student (BS), post-doc (PS) and ongoing collaborators, it has been a privilege and pleasure to edit this special issue. We would like to thank the authors for their contributions, and the team at SIGMA for initiating this issue and their invariably professional and excellent administration of the editorial process.

Bernd Schroers, Martin Speight and Paul Sutcliffe        

Papers in this Issue:

Nudged Elastic Bands and Lightly Bound Skyrmions
James Martin Speight and Thomas Winyard
SIGMA 19 (2023), 073, 26 pages   [ abs   pdf ]
Geometry of Gauged Skyrmions
Josh Cork and Derek Harland
SIGMA 19 (2023), 071, 30 pages   [ abs   pdf ]
Moduli Space for Kink Collisions with Moving Center of Mass
Christoph Adam, Chris Halcrow, Katarzyna Oles, Tomasz Romanczukiewicz and Andrzej Wereszczynski
SIGMA 19 (2023), 054, 18 pages   [ abs   pdf ]
A Skyrme Model with Novel Chiral Symmetry Breaking
Paul Sutcliffe
SIGMA 19 (2023), 051,   8 pages   [ abs   pdf ]
The Asymptotic Structure of the Centred Hyperbolic 2-Monopole Moduli Space
Guido Franchetti and Calum Ross
SIGMA 19 (2023), 043, 15 pages   [ abs   pdf ]
Solitons in the Gauged Skyrme-Maxwell Model
Leandro Roza Livramento, Eugen Radu and Yakov Shnir
SIGMA 19 (2023), 042, 17 pages   [ abs   pdf ]
Deformations of Instanton Metrics
Roger Bielawski, Yannic Borchard and Sergey A. Cherkis
SIGMA 19 (2023), 041, 11 pages   [ abs   pdf ]
Stable Kink-Kink and Metastable Kink-Antikink Solutions
Chris Halcrow and Egor Babaev
SIGMA 19 (2023), 034, 13 pages   [ abs   pdf ]

Special Issues in SIGMA

SIGMA main page