# Department of Applied Mathematics and Theoretical Physics

## 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 (2002-17).
• 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 (2006-09).
• 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.

A major recent interest has been to develop Skyrme's idea from the 1960s that atomic nuclei can be modelled as quantized solitons in a nonlinear field theory of pions. These solitons are called Skyrmions, and they have very interesting polyhedral shapes and symmetries. Larger Skyrmions are not just clusters of touching basic Skyrmions (which model protons and neutrons), but the basic Skyrmions deform and merge to some extent, as one expects physically. Improvements in computational power as well as mathematical insight has made it possible to construct and quantize Skyrmions as 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 Hamiltonian the spin excitations of a given nucleus like Carbon-12 with its isospin excitations which include Boron-12 and Nitrogen-12. Vibrational quantum states of nuclei can also be modelled using Skyrmions. This work has been in collaboration with Sir Michael Atiyah (Edinburgh), Paul Sutcliffe (Durham), Richard Battye (Manchester), Derek Harland (Leeds) and several graduate students.

About  30 years ago, while a postdoc at ITP Santa Barbara, and in collaboration with Frans Klinkhamer (now at Karlsruhe), he found unstable solitons in the Standard Model of elementary particles. Klinkhamer and Manton called these sphalerons, a name that has caught on and now has a Wikipedia entry. Sphalerons require a dynamical Higgs field, so the discovery of the Higgs boson confirms their mathematical validity, and allows one to estimate that the sphaleron energy is about 9 TeV. The probability of producing a sphaleron in particle collisions is thought to be very small, but it will be interesting to investigate this in the light of experiments at the CERN LHC on Higgs and multiple W- and Z-boson processes, when LHC achieves collisions at 14 TeV or more. Potentially, sphalerons are a source of baryon number violation, important for understanding the matter-antimatter asymmetry of the universe.

## Selected Publications

• Rational Maps, Monopoles and Skyrmions (with C.J.Houghton and P.M. Sutcliffe), Nuclear Physics B510 (1998) 507-537.
• Volume of Vortex Moduli Spaces (with S.M. Nasir), Communications in Mathematical Physics 199 (1999) 591-604.
• Asymptotic Interactions of Critically Coupled Vortices (with J.M. Speight), Communications in Mathematical Physics 236 (2003) 535-555.
• The Kähler Potential of Abelian Higgs Vortices (with H.-Y. Chen), Journal of Mathematical Physics 46 (2005) 052305.
• Superevolution, Journal of Physics A38 (2005) 6065-6079.
• Skyrmions and the ∝-Particle Model of Nuclei (with R.A. Battye and P.M. Sutcliffe), Proceedings of the Royal Society A463 (2007) 261-279.
• Solitons as Elementary Particles: A Paradigm Scrutinized, Nonlinearity 21 (2008) T221-T232.
• Skyrmions and Nuclei (with R.A. Battye and P.M. Sutcliffe), in The Multifaceted Skyrmion, eds. G.E. Brown and M. Rho, World Scientific, Singapore, 2010.
• Light Nuclei of Even Mass Number in the Skyrme Model (with R.A. Battye, P.M. Sutcliffe and S.W. Wood), Physical Review C80 (2009) 034323.
• Vortices on Hyperbolic Surfaces (with N.A. Rink), Journal of Physics A43 (2010) 434024 (also in IOP Select).
• Classical Skyrmions -- Static Solutions and Dynamics, Mathematical Methods in the Applied Sciences 35 (2012) 1188-1204.
• Geometric Models of Matter (with M.F. Atiyah and B.J. Schroers), Proceedings of the Royal Society A468 (2012) 1252-1279.
• Monopole Planets and Galaxies, Physical Review D85 (2012) 045022.
• Platonic Hyperbolic Monopoles (with P.M. Sutcliffe), Communications in Mathematical Physics 325 (2014) 821-845.
• States of Carbon-12 in the Skyrme Model (with P.H.C. Lau), Phys. Rev. Lett. 113 (2014) 232503.
• Analytic Vortex Solutions on Compact Hyperbolic Surfaces (with R. Maldonado), Journal of Physics A48 (2015) 245403.
• Scattering of Nucleons in the Classical Skyrme Model (with D. Foster), Nuclear Physics B899 (2015) 513-526.
• Electromagnetic Transition Rates for Light Nuclei in the Skyrme Model (with M. Haberichter and P.H.C. Lau), Physical Review C93 (2016) 034304.
• Dynamical $alpha$-Cluster Model of $^{16}{rm O]$ (with C.J. Halcrow and C. King), Physical Review C95 (2017) 031303(R).
• Complex Geometry of Nuclei and Atoms (with M.F. Atiyah), in Topology and Physics, eds. C.N. Yang, M.L. Ge and Y.H. He, World Scientific, 2018.
• Five Vortex Equations, Journal of Physics A50 (2017) 125403.
• Exact Gravitational Wave Signatures from Colliding Extreme Black Holes (with J. Camps and S. Hadar), Physical Review D96 (2017) 061501(R).
• Rolling Skyrmions and the Nuclear Spin-Orbit Force (with D. Harland), Nuclear Physics B935 (2018) 210-241.
• Book: Topological Solitons (with P. Sutcliffe), Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2004; paperback edition (with minor corrections), 2007.
• Book: The Physical World : An Inspirational Tour of Fundamental Physics (with N. Mee), Oxford University Press, 2017.
• 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).
• Chair, Research Meetings Committee, London Mathematical Society (2008-11).
• Management Committee of the Isaac Newton Institute (2011-present).
• Editorial Boards: Nonlinearity (1997-99), Royal Society A-side (2004-08).

## Publications

Kink moduli spaces: Collective coordinates reconsidered
NS Manton, K Oleś, T Romańczukiewicz, A Wereszczyński
– Physical Review D
(2021)
103,
025024
Kink-Antikink Interaction Forces and Bound States in a Biharmonic $φ^4$ Model
RJ Decker, A Demirkaya, NS Manton, PG Kevrekidis
– Journal of Physics A: Mathematical and Theoretical
(2020)
53,
375702
Roman Jackiw and gauge field theory: Reminiscences of mit postdoc days
N Manton
(2020)
37
Evidence for tetrahedral structure of Calcium-40
NS Manton
– International Journal of Modern Physics E
(2020)
29,
2050018
The inevitability of sphalerons in field theory
NS Manton
– Philos Trans A Math Phys Eng Sci
(2019)
377,
20180327
Iterated $φ^4$ Kinks
NS Manton, K Oleś, A Wereszczyński
– Journal of High Energy Physics
(2019)
2019,
86
Oxygen-16 spectrum from tetrahedral vibrations and their rotational excitations
CJ Halcrow, C King, NS Manton
– International Journal of Modern Physics E
(2019)
28,
1950026
Forces between kinks and antikinks with long-range tails
NS Manton
– Journal of Physics A: Mathematical and Theoretical
(2019)
52,
065401
Force between Kinks with Long-range Tails
NS Manton
(2018)
Rolling Skyrmions and the nuclear spin-orbit force
D Harland, NS Manton
– Nuclear Physics B
(2018)
935,
210
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• >

## Research Group

High Energy Physics

B2.10

01223 337879