N. S. Manton
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View article: Dynamics of excited BPS three-vortices
Dynamics of excited BPS three-vortices Open
We analyze the dynamics of Bogomol’nyi-Prasad-Sommerfield three-vortex solutions. First, for unexcited vortices, we study the two-dimensional moduli space of centered vortices with y→−y symmetry, and its metric. We identify the one-dimensi…
View article: Approach to nuclear cross sections via classical Skyrmion scattering: A proposal
Approach to nuclear cross sections via classical Skyrmion scattering: A proposal Open
By analogy with heavy ion collisions, which can be modelled by a classical hydrodynamics, it is proposed that the differential cross section for collisions of smaller nuclei can be calculated from the classical, numerical scattering data f…
View article: A $$ {\mathbbm{CP}}^2 $$ SMEFT
A $$ {\mathbbm{CP}}^2 $$ SMEFT Open
A bstract An extension of the Standard Model is proposed, where the Higgs field is valued in the complex projective plane $$ {\mathbbm{CP}}^2 $$ , rather than ℂ 2 . Its geometry is consistent with U(2) ≃ (SU(2) × U(1))/ ℤ 2 electroweak…
View article: Collective coordinate models for 2-vortex shape mode dynamics
Collective coordinate models for 2-vortex shape mode dynamics Open
Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space M, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on M, modified by a…
View article: Robustness of the hedgehog Skyrmion
Robustness of the hedgehog Skyrmion Open
A bstract We investigate the radial profile function of the hedgehog Skyrmion with unit baryon number in generic EFTs (effective field theories) of pions. The analysis assumes chiral symmetry and ignores the pion mass term. The Skyrmion is…
View article: Collective Coordinate Models for 2-Vortex Shape Mode Dynamics
Collective Coordinate Models for 2-Vortex Shape Mode Dynamics Open
Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space $M$, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on $M$, modified …
View article: Robustness of the Hedgehog Skyrmion
Robustness of the Hedgehog Skyrmion Open
We investigate the radial profile function of the hedgehog Skyrmion with unit baryon number in generic EFTs (effective field theories) of pions. The analysis assumes chiral symmetry and ignores the pion mass term. The Skyrmion is always sm…
View article: Spectral flow of vortex shape modes over the BPS 2-vortex moduli space
Spectral flow of vortex shape modes over the BPS 2-vortex moduli space Open
A bstract The flow of shape eigenmodes of the small fluctuation operator around BPS 2-vortex solutions is calculated, as a function of the intervortex separation 2 d . For the rotationally-invariant 2-vortex, with d = 0, there are three di…
View article: Integration theory for kinks and sphalerons in one dimension
Integration theory for kinks and sphalerons in one dimension Open
The static kink, sphaleron and kink chain solutions for a single scalar field φ in one spatial dimension are reconsidered. By integration of the Euler–Lagrange equation, or through the Bogomolny argument, one finds that each of these solut…
View article: Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space
Spectral Flow of Vortex Shape Modes over the BPS 2-Vortex Moduli Space Open
The flow of shape eigenmodes of the small fluctuation operator around BPS 2-vortex solutions is calculated, as a function of the intervortex separation $2d$. For the rotationally-invariant 2-vortex, with $d = 0$, there are three discrete m…
View article: Neumann boundary condition for Abelian BPS vortices
Neumann boundary condition for Abelian BPS vortices Open
A bstract We study abelian BPS vortices on a surface S with boundary, which satisfy the Neumann boundary condition on the norm of the scalar field, or equivalently, that the current along the boundary vanishes. These vortices have quantise…
View article: Neumann Boundary Condition for Abelian Vortices
Neumann Boundary Condition for Abelian Vortices Open
We study abelian BPS vortices on a surface $S$ with boundary, which satisfy the Neumann boundary condition on the norm of the scalar field, or equivalently, that the current along the boundary vanishes. These vortices have quantised magnet…
View article: Simplest oscillon and its sphaleron
Simplest oscillon and its sphaleron Open
Oscillons in a simple, one-dimensional scalar field theory with a cubic potential are discussed. The theory has a classical sphaleron, whose decay generates a version of the oscillon. A good approximation to the small-amplitude oscillon is…
View article: Quantum statistical mechanics of dissolving Abelian Higgs vortices
Quantum statistical mechanics of dissolving Abelian Higgs vortices Open
The quantum partition function for Abelian Higgs vortices at high density—the regime of dissolving vortices—is calculated explicitly, using spectral data for the Beltrami Laplacian on the N -vortex moduli space with a scaled Fubini–…
View article: Wormhole Model for Neon-20
Wormhole Model for Neon-20 Open
A quantum mechanical model for the Neon-20 nucleus is developed that allows for the splitting of a bipyramidal structure of five alpha-partices into an alpha-particle and an Oxygen-16 nucleus. The geometry of the configuration space is ass…
View article: Quantum statistical mechanics of vortices
Quantum statistical mechanics of vortices Open
The asymptotic partition function for quantized abelian Higgs vortices at high temperature T is found to leading and subleading order, and from this the equation of state of the vortex gas is derived, including the first quantum correction…
View article: Relativistic moduli space for kink collisions
Relativistic moduli space for kink collisions Open
The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by exp…
View article: Kink moduli spaces: Collective coordinates reconsidered
Kink moduli spaces: Collective coordinates reconsidered Open
Moduli spaces - finite-dimensional, collective coordinate manifolds - for\nkinks and antikinks in $\\phi^4$ theory and sine-Gordon theory are reconsidered.\nThe field theory Lagrangian restricted to moduli space defines a reduced\nLagrangi…
View article: Tetrahedral intrinsic structure of Oxygen-16 revisited
Tetrahedral intrinsic structure of Oxygen-16 revisited Open
A model for vibrational and rotational excitations of an intrinsic tetrahedral structure of the Oxygen-16 nucleus has been investigated, building on classic work of Wheeler, Dennison and Robson. Tetrahedral A- and F-phonons are treated har…
View article: Kink-Antikink Interaction Forces and Bound States in a Biharmonic $ϕ^4$ Model
Kink-Antikink Interaction Forces and Bound States in a Biharmonic $ϕ^4$ Model Open
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $ϕ^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as a f…
View article: Kink-Antikink Interaction Forces and Bound States in a Biharmonic $\phi^4$ Model
Kink-Antikink Interaction Forces and Bound States in a Biharmonic $\phi^4$ Model Open
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $\phi^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as …
View article: Nonlinearity, Geometry and Field Theory Solitons
Nonlinearity, Geometry and Field Theory Solitons Open
Topological solitons occur in many types of nonlinear field theory. Their motion and interactions can be simulated classically, and can be well approximated by a finite-dimensional dynamics on a moduli space of collective coordinates. Inte…
View article: Forces between kinks and antikinks with long-range tails
Forces between kinks and antikinks with long-range tails Open
In a scalar field theory with a symmetric octic potential having a quartic minimum and two quadratic minima, kink solutions have long-range tails. We calculate the force between two kinks and between a kink and an antikink when their long-…
View article: Force between Kinks with Long-range Tails
Force between Kinks with Long-range Tails Open
In a scalar field theory that has a symmetric octic potential with a quartic minimum and two quadratic minima, kink and mirror kink solutions have long-range tails. We calculate the force between these kinks when their long-range tails ove…
View article: Quantized Skyrmions from SU(4) weight diagrams
Quantized Skyrmions from SU(4) weight diagrams Open
Starting from solutions of the lightly bound Skyrme model, we construct many new Skyrmion solutions of the standard Skyrme model with tetrahedral or octahedral symmetry. These solutions are closely related to weight diagrams of the group S…
View article: Exact gravitational wave signatures from colliding extreme black holes
Exact gravitational wave signatures from colliding extreme black holes Open
The low-energy dynamics of any system admitting a continuum of static\nconfigurations is approximated by slow motion in moduli (configuration) space.\nHere, following Ferrell and Eardley, this moduli space approximation is\nutilized to stu…
View article: Lightly Bound Skyrmions, Tetrahedra and Magic Numbers
Lightly Bound Skyrmions, Tetrahedra and Magic Numbers Open
In the lightly bound Skyrme model, several Skyrmions having particularly strong binding are clusters of unit baryon number Skyrmions arranged as truncated tetrahedra. Their baryon numbers form the sequence B = 4, 16, 40, 80, 140, 224. This…