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Dr Derek G Harland

Associate Professor in Geometry
Pure Mathematics

Contact details

Room: 8.06
Tel: +44 (0)113 3435152
Email: D.G.Harland @ leeds.ac.uk

Keywords

Topological solitons
Gauge theory
Monopoles
Instantons
Skyrmions

Research interests

In theoretical physics and in differential geometry one often encounters the problem finding minima of an "energy functional" defined over an infinite-dimensional configuration space. Typically the configuration space might be a space of maps between manifolds, or a space of connections on and sections of a vector bundle. The study of such critical points may provide non-trivial information about the underlying manifolds and the physics involved. Two systems I am currently interested in are the Yang-Mills-Higgs, Yang-Mills and Skyrme energy functionals, whose critical points are called "monopoles", "instantons" and "skyrmions" respectively. Some of my recent work has looked at such systems on manifolds of relatively high dimension.

Useful links

Personal website

Current postgraduate students

Joshua Cork (2014)

Publications

Harland D, Nogradi D On the charge density and asymptotic tail of a monopole JOURNAL OF MATHEMATICAL PHYSICS, 57, 2016
DOI:10.1063/1.4941982

Bolognesi S, Harland D, Sutcliffe P Magnetic bags in hyperbolic space Physical Review D - Particles, Fields, Gravitation and Cosmology, 92, 2015
DOI:10.1103/PhysRevD.92.025052
View abstract

Gillard M, Harland D, Speight M Skyrmions with low binding energies Nuclear Physics B, 895, 272-287, 2015
DOI:10.1016/j.nuclphysb.2015.04.005
View abstract

Harland D Topological energy bounds for the Skyrme and Faddeev models with massive pions Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 728, 518-523, 2014
DOI:10.1016/j.physletb.2013.11.062
View abstract

Harland D, Jäykkä J, Shnir Y, Speight M Isospinning hopfions Journal of Physics A: Mathematical and Theoretical, 46, 2013
DOI:10.1088/1751-8113/46/22/225402
View abstract

Dooley S, McCrossan F, Harland D, Everitt MJ, Spiller TP Collapse and revival and cat states with an N-spin system Physical Review A - Atomic, Molecular, and Optical Physics, 87, 2013
DOI:10.1103/PhysRevA.87.052323
View abstract

Harland D, Everitt MJ, Nemoto K, Tilma T, Spiller TP Towards a complete and continuous Wigner function for an ensemble of spins or qubits Physical Review A - Atomic, Molecular, and Optical Physics, 86, 2012
DOI:10.1103/PhysRevA.86.062117
View abstract

Harland D, Palmer S, Sämann C Magnetic domains Journal of High Energy Physics, 2012
DOI:10.1007/JHEP10(2012)167
View abstract

Foster D, Harland D Helical buckling of Skyrme-Faddeev solitons Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468, 3172-3190, 2012
DOI:10.1098/rspa.2012.0132
View abstract

Harland D, Nölle C Instantons and Killing spinors Journal of High Energy Physics, 2012
DOI:10.1007/JHEP03(2012)082
View abstract

Harland D, Popov AD Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure Journal of High Energy Physics, 2012
DOI:10.1007/JHEP02(2012)107
View abstract

Harland DG The large N limit of the Nahm transform Communications in Mathematical Physics, 311, 689-712, 2011
DOI:10.1007/s00220-011-1378-7

Harland D, Speight M, Sutcliffe P Hopf solitons and elastic rods PHYSICAL REVIEW D, 83, 2011
DOI:10.1103/PhysRevD.83.065008

Harland D, Speight M, Sutcliffe P Hopf solitons and elastic rods Physical Review D - Particles, Fields, Gravitation and Cosmology, 83, 2011
DOI:10.1103/PhysRevD.83.065008
View abstract

Harland DG, Ivanova TA, Lechtenfeld O, Popov AD Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons Communications in Mathematical Physics, 300, 185-204, 2010
DOI:10.1007/s00220-010-1115-7

Harland D Kinks, chains, and loop groups in theℂℙn sigma models Journal of Mathematical Physics, 50, 2009
DOI:10.1063/1.3266172
View abstract

Harland D, Kürkçüoǧlu S Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices Nuclear Physics B, 821, 380-398, 2009
DOI:10.1016/j.nuclphysb.2009.06.031
View abstract

Harland D, Ward RS Dynamics of periodic monopoles Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 675, 262-266, 2009
DOI:10.1016/j.physletb.2009.03.074
View abstract

Harland D, Ward RS Chains of skyrmions JOURNAL OF HIGH ENERGY PHYSICS, 2008

Harland D Hyperbolic calorons, monopoles, and instantons Communications in Mathematical Physics, 280, 727-735, 2008
DOI:10.1007/s00220-008-0471-z
View abstract

Harland D, Ward RS Walls and chains of planar Skyrmions Physical Review D - Particles, Fields, Gravitation and Cosmology, 77, 2008
DOI:10.1103/PhysRevD.77.045009
View abstract

Harland D Large scale and large period limits of symmetric calorons Journal of Mathematical Physics, 48, 2007
DOI:10.1063/1.2768186
View abstract

Charbonneau B, Harland D Deformations of nearly Kähler instantons Communications in Mathematical Physics
DOI:10.1007/s00220-016-2675-y
View abstract