# School of Mathematics

## 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

## Current postgraduate students

Joshua Cork (2014)

Ben Daniel-Thorpe (2016)

Joe Driscoll (2016)

## Publications

**Charbonneau B, Harland D** Deformations of Nearly Kähler Instantons *Communications in Mathematical Physics*, **348**, 959-990, 2016

DOI:10.1007/s00220-016-2675-y

View abstract

**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

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