# Professor Nick Manton

## Career

• Postdoctoral Appointments: ENS, Paris; MIT; ITP Santa Barbara; St John's College, Cambridge (1978-87).
• University Appointments in DAMTP: University Lecturer (1987-94), Reader (1994-98), Professor of Mathematical Physics (1998-present).
• Head, High Energy Physics group, DAMTP (2002-present).
• Member of Council, School of the Physical Sciences (2007).
• Fellow of St John's College (1997-present), Director of Studies in Applied Mathematics (1997-98), Member of College Council (2006-present).
• Junior Whitehead Prize, London Mathematical Society, 1991.
• Fellow of the Royal Society, 1996.

## Research

Nick Manton's research interests cover broad areas of theoretical and mathematical physics, in particular, classical and quantum field theory applied to particle and nuclear physics. The majority of his work has been on topological solitons in field theory, which include vortices, monopoles, instantons and Skyrmions. He proposed and developed the theory of non-relativistic soliton dynamics based on the geometry of soliton moduli spaces; this is called the geodesic approximation to soliton dynamics. Some recent work, using a variant of Ricci flow, has elucidated the K\"ahler geometry of vortex moduli spaces.

A major recent interest has been to develop Skyrme's idea from the 1960s that atomic nuclei can be modelled as solitons in a nonlinear field theory of pions. These solitons are called Skyrmions, and they have very interesting polyhedral shapes. Improvements in computational power as well as mathematical insight has made it possible to construct and quantize Skyrmions as large as those needed to model Carbon-12 and Oxygen-16. The spins and energies of nuclear ground states and excited states are described quite well by Skyrmions. Compared with other nuclear models, the Skyrme model manages to unify into the spectrum of a single "rigid-body" Hamiltonian the spin excitations of a given nucleus like Carbon-12 with its isospin excitations which include Boron-12 and Nitrogen-12. This work has been in collaboration with Sir Michael Atiyah (Edinburgh), Paul Sutcliffe (Durham), Richard Battye (Manchester) and others.

More than 20 years ago, in collaboration with Frans Klinkhamer (Karlsruhe), he found unstable solitons in the standard electroweak theory of elementary particles. They called these sphalerons, a name that has caught on and now has a Wikipedia entry. Their status and significance will need to be revisited in the light of forthcoming results from the CERN LHC on the Higgs particle, and multiple W- and Z-boson processes. Potentially, they are a source of baryon number violation, important for understanding the matter-antimatter asymmetry of the universe.

## Selected Publications

• On the Constraints defining BPS Monopoles (with C.J. Houghton and N.M. Rom\~ao), Communications in Mathematical Physics 212 (2000) 219-243.
• Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair (with A.J. Bordner and R. Sasaki), Progress of Theoretical Physics 103 (2000) 463-487.
• Classical Supersymmetric Mechanics (with R. Heumann), Annals of Physics 284 (2000) 52-88.
• Asymptotic Interactions of Critically Coupled Vortices (with J.M. Speight), Communications in Mathematical Physics 236 (2003) 535-555.
• The Dynamics of Vortices on $S2$ near the Bradlow Limit (with J.M. Baptista), Journal of Mathematical Physics 44 (2003) 3495-3508.
• The Interaction Energy of Well-separated Skyrme Solitons (with B.J. Schroers and M.A. Singer), Communications in Mathematical Physics 245 (2004) 123-147.
• The K\"ahler Potential of Abelian Higgs Vortices (with H.-Y. Chen), Journal of Mathematical Physics 46 (2005) 052305.
• The Energy of Scattering Solitons in the Ward Model (with T. Ioannidou), Proceedings of the Royal Society A 461 (2005) 1965-1973.
• Reduced Dynamics of Ward Solitons (with M. Dunajski), Nonlinearity 18 (2005) 1677-1689.
• Superevolution, Journal of Physics A38 (2005) 6065-6079.
• Skyrmions and the $\alpha$-Particle Model of Nuclei (with R.A. Battye and P.M. Sutcliffe), Proceedings of the Royal Society A 463 (2007) 261-279.
• Reparametrising the Skyrme Model using the Lithium-6 Nucleus (with S.W. Wood), Physical Review D74 (2006) 125017.
• Skyrmions and Nuclei, in The Many Facets of Geometry: a Tribute to Nigel Hitchin, Oxford University Press (to appear).
• Light Nuclei as Quantized Skyrmions (with O.V.Manko and S.W.Wood), Physical Review C76 (2007) 055203.
• One-Vortex Moduli Space and Ricci Flow, Journal of Geometry and Physics, published online 2008.
• Solitons as Elementary Particles: A Paradigm Scrutinized, Nonlinearity [Open Problem] 21 (2008) T221-T232.
• Scaling Identities for Solitons beyond Derrick's Theorem. arXiv: 0809.2891 (2008).
• Light Nuclei as Quantized Skyrmions: Energy Spectra and Form Factors (with S.W. Wood). Submitted to the Proceedings of the 15th Annual Seminar Quarks 2008, Sergiev Posad, Russia.
• Book: Topological Solitons (with P. Sutcliffe), Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2004; paperback edition (with minor corrections), 2007.
• Editorial: Special issue on Integrability, Topological Solitons and Beyond (coedited with A.S. Fokas), Journal of Mathematical Physics 44 (8) (2003) 3147-3673.

## External Activities

• Programme Committee of the International Centre for Mathematical Sciences, Edinburgh (2005-08).
• Research Meetings Committee (chair), London Mathematical Society (2008-present).
• Editorial Boards: Nonlinearity (1997-99), Royal Society A-side (2004-08).
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