Dynamics near relative equilibria: Nongeneric momenta at a 1:1 group-reduced resonance

An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some of the shape variables couple to the group variables to first order in the momentum perturbation, and the first order perturbation theory implies that the relative equilibrium slowly changes orientation in the same way that a charged particle with magnetic moment moves on a sphere under the influence of a radial magnetic monopole. In the course of showing this a normal form is constructed for linearizations of relative equilibria and for Hamiltonians near group orbits of relative equilibria. Received August 27, 1998; in final form February 20, 1999     

On the existence of Skyrme gauge field monopoles

In this paper, we study Skyrme-like monopoles which are topological solitons in three space dimensions. We prove the existence of symmetric monopole solutions in a gauged Skyrme model by a variational method. We also obtain some properties of the energy-minimizing solutions. For when the Skyrme coupling constant κ=0, we arrive at the BPS monopole equations. Furthermore, we obtain the relation between the BPS and non-BPS monopole solutions, and properties of the BPS monopole solution.     

Hyperbolic Monopoles and Holomorphic Spheres

We associate to an SU(2) hyperbolic monopole a holomorphicsphere embedded in projective space and use this to uncovervarious features of the monopole.     

A Simplified Model for Monopole Catalysis of Nucleon Decay

We present a simple model where a nucleon is treated as a skyrmion, both the monopole and skyrmion are smooth solutions of the classical field equations, the baryon number nonconservation is explicitly built in and is due to the classical analogue of the triangle anomaly, and there is no necessity to consider leptons. We show by numerical analysis that there are no static classical solutions with a nonzero baryon number on top of the monopole, i.e., that the monopole catalysis of skyrmion decay indeed proceeds classically.     

The ABCs of Magnetic Monopole Dynamics

We revisit the explicit solution of Newton's equation of motion (mass times acceleration equals force) for a (pointlike, massive) magnetic monopole moving in the Coulomb field of a (fixed, pointlike) electric charge or, equivalently, of a (pointlike, massive) electric charge moving in the magnetic field of a (fixed) magnetic monopole.     

An Existence Proof for the Gravitating BPS Monopole

We prove the existence of the gravitating BPS monopole in Einstein-Yang-Mills-Higgs (EYMH) theory. Existence is established using a Newtonian perturbation argument which shows that a Yang-Mills-Higgs BPS monopole solution can be be continued analytically in powers of 1/c² to an EYMH solution. Communicated by Sergiu Klainerman submitted 2/04/04, accepted 29/08/05     

Monopole solutions as three-dimensional generalizations of Kronecker series

We investigate the Dirac monopole on a three-dimensional torus as a solution of the Bogomolny equations with nontrivial boundary conditions. We show that a suitable analytic continuation of the obtained solution is a three-dimensional generalization of the Kronecker series, satisfies the corresponding functional equation, and is invariant under modular transformations.     

Three-dimensional superconformal field theories, indices, and monopoles

We explain the recent progress in three-dimensional superconformal field theories based on the index for magnetic monopole operators and discuss applications to M2-branes and the AdS/CFT duality.     

Quantum generalized Toda system

We construct a ??spectral curve?? for the generalized Toda system, which allows efficiently finding its quantization. In turn, the quantization is realized using the technique of the quantum characteristic polynomial for the Gaudin system and an appropriate Alder-Kostant-Symes reduction. We also discuss some relations of this result to the recent consideration of the Drinfeld Zastava space, the monopole space, and corresponding symmetries of the Borel Yangian.     

Minnaert resonances for acoustic waves in bubbly media

Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.     

Seiberg-Witten invariants, the topological degree and wall crossing formula

Following S. Bauer and M. Furuta we investigate finite dimensional approximations of a monopole map in the case b ₁ = 0. We define a certain topological degree which is exactly equal to the Seiberg-Witten invariant. Using homotopy invariance of the topological degree a simple proof of the wall crossing formula is derived.     

基金投资行为与投资绩效实证研究

本文主要研究2000年末到2004年6月国内基金投资行为与投资绩效。我们将基金交易行为分为:新进入、完全退出和对仓位进行调整3类,并分别研究其投资行为。研究结果显示,我国基金交易频率很高,近90%的基金采用动量投资策略,基金新进入股票时动量效应最强。价值型基金更易采取动量投资策略,高动量组收益高于低动量组收益。     

Quantum entropy of Dirac fields in black holes

We use the brick-wall model to study the quantum entropy of the Dirac field in a static black hole with a global monopole or a cosmic string. We show that the entropy of the Dirac field contains a quadratically divergent term and two logarithmically divergent ones and it is not proportional to the entropy of the scalar field. The contribution of the logarithmic term to the entropy depends on the black-hole characteristics and is always negative. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 60–64, October, 2006.     

Construction of Euclidian Monopoles

This paper describes a procedure for the construction of monopoleson three-dimensional Euclidean space, starting from their rationalmaps. A companion paper, ‘Euclidean monopoles and rationalmaps’, to appear in the same journal, describes the assignmentto a monopole of a rational map, from CP¹ to a suitable flagmanifold. In describing the reverse direction, this paper completesthe proof of the main theorem therein. A construction of monopoles from solutions to Nahm's equations(a system of ordinary differential equations) has been well-knownfor certain gauge groups for some time. These solutions arehard to construct however, and the equations themselves becomeincreasingly unwieldy when the gauge group is not SU(2). Here, in contrast, a rational map is the only initial data.But whereas one can be reasonably explicit in moving from Nahmdata to a monopole, here the monopole is only obtained fromthe rational map after solving a partial differential equation. A non-linear flow equation, essentially just the path of steepestdescent down the Yang-Mills-Higgs functional, is set up. Itis shown that, starting from an ‘approximate monopole’- constructed explicitly from the rational map - a solutionto the flow must exist, and converge to an exact monopole havingthe desired rational map. 1991 Mathematics Subject Classification:53C07, 53C80, 58D27, 58E15, 58G11.     

Monopole Blocking Governed by a Modified KdV Type Equation

A type of coupled variable coefficient modified Korteweg-de Vries system is derived from a two-layered fluid system. It is known that the formation, maintenance, and collapse of an atmospheric blocking are always related with large-scale weather or short term climate anomalies. One special analytical solution of the obtained system successfully features the evolution cycle of an atmospheric monopole type blocking event. In particular, our theoretical results capture a real monopole type blocking case that happened during 19 February 2008 to 26 February 2008 can be well described by our analytical solution.     

Monopoles, particles and rational functions

We prove a recent conjecture of Manton and Murray: if a polynomialp(z) of degreek — 1 is given, then anSU (2) monopole corresponding to a rational functionp(z)/q(z) with well-separated poles \₁,...,\_k is approximately made up from charge 1 monopoles located at points (1/2 In p(\_i), \_i). We show how the rate of approximation changes with the numeratorp(z) with the result that, as long as the values of the numerator remain close together relative to the distances between poles, the above statement remains true and ceases to be so otherwise.We also show that the spectral curve of the monopole approaches the union of curves of charge 1 monopoles exponentially fast. This remains true forSU (N) monopoles.     

Yang-Mills-Higgs soliton dynamics in 2+1 dimensions

Dimensional reduction of the self-dual Yang-Mills equation in 2+2 dimensions produces an integrable Yang-Mills-Higgs-Bogomolnyi equation in 2+1 dimensions. For theSU(1,1) gauge group, a t'Hooft-like ansatz is used to construct a monopole-like solution and an N-soliton-type solution, which describes both the static deformed monopoles and the exotic monopole dynamics including a transmutation. How the monopole solution results from the twistor formalism is shown. Multimonopole solutions are commented on. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 339–350, December, 1998.     

Existence of Dyons in the Coupled Georgi�CGlashow�CSkyrme Model

We prove the existence of a continuous family of finite-energy particle-like solutions in the coupled Georgi–Glashow–Skyrme model carrying both electric and magnetic charges, known as dyons. Due to the presence of electricity and the Minkowski spacetime signature, we need to solve a variational problem with an indefinite action functional. Our results show that, while the magnetic charge is uniquely determined by the topological monopole number, the electric charge of a solution can be arbitrarily prescribed in an open interval.