Self-dual monopoles and toda molecules

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.     

Self-dual monopoles in a seven-dimensional gauge theory

The existence of self-dual or anti-self-dual monopoles of a seven-dimensional generalized Yang-Mills-Higgs theory is proved using the second-order equations of motion. The behavior of solutions can be used to recognize self- or anti-self-duality. Moreover, it is shown that, in the class of the field configurations under discussion, the solutions are, in fact, unique.     

Colored magnetic monopoles

We extend Dirac's theory of magnetic monopoles to the case of non-Abelian color gauge groups. Exact classical solution is obtained by making use of the gauge-independent method of Yang-Mills field. The case of broken gauge symmetry is also briefly discussed.     

Non-Abelian magnetic monopoles

It is shown that a general, irreducible, SU(n), Sp(n), SO(2n) monopole with maximal symmetry breaking is determined by its spectral data. For SU(n) with minimal symmetry breaking the spectral data is defined and also shown to determine the monopole.Research supported in part by NSF Grant 8120790     

Introduction to magnetic monopoles

One of the most basic properties of magnetism is that a magnet always has two poles, north and south, which cannot be separated into isolated poles, i.e. magnetic monopoles. There are strong theoretical arguments why magnetic monopoles should exist, but in spite of extensive searches they have never been found. This article gives an introduction to theoretical and experimental aspects of magnetic monopoles and discusses their role in our understanding of fundamental physics, both historically and today.     

Geometrical aspects of magnetic monopoles

The possible topological structures of elementary particles have been investigated to explore the possibility of the existence of magnetic monopoles. It is pointed out that when an elementary charged particle is depicted as an extended body such that the orientation of the internal space (internal helicity) defines the fermion number, the global conservation of this does not allow the existence of a magnetic monopole. Again it is argued that when anisotropy is introduced in the microlocal space-time depicting the internal space of hadrons, this gives rise to the internal symmetry algebra and no non-Abelian gauge fields and Higgs scalars are necessary to have a grand unified scheme of interactions. This avoids theSU ₂ and GUT monopoles. Besides, in this formalism, baryon number corresponds to the orientation or internal helicity of the composite system and the global conservation of this quantum number is found to be a consequence of Lorentz invariance. This forbids the existence of any sort of cosmological monopole in this Lorentz invariant Universe.     

Galilean invariance and magnetic monopoles

The existence of Dirac monopoles is shown to be incompatible with Galilean invariance. A discussion follows on the interpretation of monopoles physics in a Galilean approximation.     

Composite gluons and magnetic monopoles

We present a static solution to the classical field equations of a purely spinorial model with SU(2) internal symmetry. The model contains composite vector and pseudovector gluon fields. The solution for the vector field is precisely that of the Wu-Yang monopole.     

Dual electromagnetism and magnetic monopoles

Dual electromagnetism (proposed some time ago) allows the fractional electric charges and the magnetic monopoles to exist simultaneously. In fact, the Dirac quantization condition can be numerically reduced (with some plausible assumptions) to the third component of the particle total weak isospin, which by definition is always quantized. The field angular momentum,L, of a static particle-magnetic monopole configuration is evaluated exactly; it is found that because the dual photon has a mass,M _c ,L generally depends onr, the separation between a particle and a monopole. However, sinceM _c - 130 GeV, atr > M _c ^–1 ,L is basically dominated by ordinary electromagnetism and as such very weakly dependent onr.     

寻找磁单极子

电和磁遍布现代社会方方面面,构成了现有大部分科学技术的基础。因此大家倾向于认为这些效应已经被充分理解,不存在基础物理层面的未解之谜。诚然,在绝大多数应用场合,这些磁电效应可以用James Clerk Maxwell 在1864 年归纳的Maxwell 方程描述。从更深的层次上,这些效应可以从量子电动力学的角度——粒子物理标准模型的一部分,得到自洽解释。该理论工作如此之好以至于它能准确给出电子磁偶极矩的前10 位有效数字。尽管如此,现有电磁学还存在一个我们所不能理解的基础问题——有关磁单极子的问题。     

Spherical symmetry and magnetic monopoles

I give a general, gauge-invariant, definition of spherical symmetry in a gauge theory. I show that if the fields are required to be non-singular at the origin, such symmetry can occur only for certain values of the magnetic charge. One consequence is the existence of stable monopoles which are not spherically symmetric.     

The fate of primordial magnetic monopoles

Unified gauge theories, in which the SU (2)_L and U (1)_Y subgroups do not have non-trivial intersections, possess an in-built mechanism for a complete extinction of the primordial magnetic monopoles. The potential conflict with the standard hot big bang cosmology is therefore avoided in such theories. The usual gauge theories, based on SU (5), SO (10) and E₆ do not have this property.     

A classification ofSU 3 magnetic monopoles

A classification scheme is proposed forSU ₃ magnetic monopoles when the Higgs fields lie in the adjoint representation. The scheme is based on a study of the second homotopy groups of the orbit spaces.     

A path-dependent approach to colored magnetic monopoles

We extend Abelian gauge theory of magnetic monopoles to the non-Abelian case, by means of Mandelstam's path-dependent approach to Yang-Mills fields. In this framework, theSU(3) generalization of Dirac's relationship plays the role of a consistency condition for the theory.     

Bäcklund transformations and magnetic monopoles

We show that a recent solution of an SU(2) gauge theory, claimed to be a 3-monopole solution, is in fact an infinite-energy solution.