Nicholas S. Manton

Space-time symmetries in gauge theories

A general definition of symmetries of gauge fields is proposed and a method developed for constructing symmetric fields for an arbitrary gauge group. Scalar fields occur naturally in the formalism and the pure gauge theory reduces to a Higgs model in lower dimensions.

A new six-dimensional approach to the Weinberg-Salam model

Abstract The bosonic sector of the Weinberg-Salam model is derived from a 6-dimensional Yang-Mills theory by imposing rotational symmetry in the extra, compact dimensions. The Weinberg angle and the mass of the Higgs particle are predicted.

Classical and Quantum Dynamics of BPS Monopoles

Abstract The dynamics of two non-relativistic BPS monopoles is described using the Atiyah-Hitchin metric on the space of collective coordinates of the monopoles. M . Classical orbits correspond to geodesics on M . Quantum states are obtained by supposing the hamiltonian is proportional to the covariant laplacian on M . We analyse in detail the asymptotic equations describing monopoles whose separation is large compared with the individual monopole radii. These give a non-trivial generalization of the Coulomb problem and are exactly soluble both in the classical and quantum regime. A variety of scattering processes and bound states are described.

Rational Maps, Monopoles and Skyrmions

We discuss the similarities between BPS monopoles and Skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to construct good approximations to several known Skyrmions, including all the minimal energy configurations up to baryon number nine, and some new solutions such as a baryon number seventeen Skyrme field with the truncated icosahedron structure of a buckyball. The new approach is also used to understand the low-lying vibrational modes of Skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rational maps which may be of use in understanding the Sen forms on the monopole moduli spaces.

Skyrmions from instantons

Abstract Skyrme field configurations in R 3 may be generated from SU(2) instantons in R 4 by computing the holonomy along lines parallel to the time-axis. Some of these are good approximations to important configurations for one-and two-baryon physics.

Geometry of Skyrmions

A Skyrmion may be regarded as a topologically non-trivial map from one Riemannian manifold to another, minimizing a particular energy functional. We discuss the geometrical interpretation of this energy functional and give examples of Skyrmions on various manifolds. We show how the existence of conformal transformations can cause a Skyrmion on a 3-sphere to become unstable, and how this may be related to chiral symmetry breaking.

The moduli space metric for well-separated BPS monopoles

The Lagrangian for the motion of n well-separated BPS monopoles is calculated, by treating the monopoles as point particles with magnetic, electric and scalar charges. It can be reinterpreted as the Lagrangian for geodesic motion on the asymptotic region of the n-monopole moduli space, thereby determining the asymptotic metric on the

Pair Production at Strong Coupling in Weak External Fields

The rate of electron-positron pair production in a weak external electric field at large values of e is computed. The method is extended to compute the rate of monopole-antimonopole pair production in a weak external magnetic field at large magnetic charge.

Complex structure of monopoles

Abstract Instanton techniques are applied to the classical monopole equations. The Prasad-Sommerfield monopole is rederived in a curious way, and new complex solutions are found, representing a distorted monopole

Skyrmions in flat space and curved space

Abstract The skyrmion in flat space is compared with the form it would have if space were a three-sphere. On a sphere of a critical radius, the skyrmion attains a topological lower bound on the energy and satisfies a set of first-order equations.