Magnetic monopoles

These are notes of the first part of the lectures given at the JINR-ISU Baikal Summer School on Physics of Elementary Particles and Astrophysics (July 2010). I review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory providing a pedagogical introduction into to the theory of non-Abelian monopoles both in the BPS limit and beyond of it. I briefly discuss monopole dynamics, the idea of the moduli space and some of the basic properties which are connected with the field theoretical aspects of these classical solutions.     

Magnetic monopoles

Summary Theoretical foundations for the existence of magnetic monopoles are given. Consequences extracted from cosmological and astrophysical considerations on the abundance of magnetic monopoles today are reviewed. The latest experimental results in the search for classical monopoles as well as for grand unified monopoles are summarized.

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Riassunto Si danno i fondamenti teorici per l'esistenza di monopoli magnétici. Si esaminano le conseguenze tratte da considerazioni cosmologiche e astrofisiche sull'abbondanza di monopoli magnetici attuale. Si riassumono i piú recenti risultati sperimentali sulla ricerca di monopoli classici e di quelli della grande unificazione.

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Резюме Приводятся теоретические обоснования сушствования магнитных монополей. Анализируются следствия из космологических и астрофизических рассмотрений, касающиеся распространенноси магнитных мононолей в настоящее время. Приводятся последние экспериментальные результаты по поискы классических монополей и монополей Великого Объединения.

     

Magnetic monopoles in gauge theories

Magnetic monopoles in gauge theories are investigated. Let G be the gauge group and H the group of symmetries which are not spontaneously broken. The existence of magnetic monopoles is proved in the case when the group G has a compact covering group but the covering group of H is non-compact.     

Magnetic monopoles in ferromagnetic materials

The interactions of slow $\text{(10}{}^{\mathrm{?5}}\text{? v/c ? 10}{}^{\mathrm{?2}}\text{)}$ magnetic monopoles with ferromagnetic materials are studied. The spin-flip cross section σ and the energy loss dE/dx are calculated for magnetic monopoles impinging parallel to the magnetization direction. In iron, these reach a maximum at v/c ～ 3 × 10^?4, where they take the value of 100 Ų and 100 MeV/cm respectively. The electromagnetic signal of a monopole passing through a ferromagnet and the generation of spin waves are discussed.     

Magnetic monopoles, alive

We review recent developments in understanding the physics of the magnetic monopoles in unbroken non-Abelian gauge theories. Since numerical data on the monopoles are accumulated in lattice simulations, the continuum theory is understood as the limiting case of the lattice formulation. We emphasize physical effects related to the monopoles. In particular, we discuss the monopole-antimonopole potential at short and larger distances as well as a dual formulation of the gluodynamics, relevant to the physics of the confinement.     

Hyperons in neutron stars

Generalized beta equilibrium involving nucleons, hyperons and isobars is examined for neutron star matter. The hyperons produce a considerable softening of the equation of state. It is shown that the observed masses of neutron stars can be used to settle a recent controversy concerning the nuclear compressibility. Compressibilities less than 200 MeV are incompatible with observed masses.     

Abnormal neutron stars

Quasi-classical field theory is used to predict abnormal behaviour of neutron matter in a model with neutrons, scalar mesons and vector mesons. We predict two stable families of neutron stars, a conventional one and an unconventional one with surface density in excess of 10¹⁵g cm^?3, roughly.     

Superfluidity in neutron stars

Arguments are presented to show that the BCS theory of superfluidity in its original form may not be applicable to neutron star matter over a wide range of density.     

Magnetic monopoles with no strings

Previous treatments of the charge-monopole system have used either a lagrangian singular along the Dira string or a multiple valued action integral. Here we formulate an action principle for this system which involves no strings and is single. This is achieved by writing the lagrangian directly in terms of the variables of a suitable fibre bundle. Canonical quantization is carried out in a simple way and known results are recovered.     

X-rays from neutron stars

The basic theoretical ideas in the models of regularly pulsating X-ray sources are discussed, and put in relation to the observations. The topics covered include physics of the magnetosphere of an accreting neutron star, hydrodynamics of the accretion column, physical processes close to the surface of the neutron star such as proton-electron collisions, photon-electron interactions.     

Magnetic monopoles and tachyons in special relativity

The mere special relativity does not explicitly predict existence of (sub-luminal) monopoles, but on the contrary explicitly predicts existence of super-luminal (tachyon) monopoles, with magnetic charge about 100 times less than usually assumed. This fact is relevant also at the light of current experiments looking for magnetic poles.     

Magnetic monopoles and non-Abelian gauge theories

We review some properties of magnetic monopoles in non-Abelian gauge theories. Removal of Dirac string singularities and generalizations of the Wu-Yang solution that follow from this procedure are described. A discussion of the possible relevance of monopoles in strong interaction models and their role in quark confinement schemes is given. The magnetic monopole soliton discovered by 't Hooft and Polyakov, the first order formalism developed by Bogomolny, and extensions of these ideas are illustrated.Work supported in part by the U.S. Energy Research and Development Administration under Contract No. EY-76-C-02-2232B^*000.     

f-Mode instability in relativistic neutron stars

We present the first calculation of the basic properties of the f-mode instability in rapidly rotating relativistic neutron stars, adopting the Cowling approximation. By accounting for dissipation in neutron star matter, i.e., shear or bulk viscosity and superfluid mutual friction, we calculate the associated instability window. For our specific stellar model, a relativistic polytrope, we obtain a minimum gravitational growth time scale (for the dominant ?=m=4 mode) of the order of 10(3)-10(4) s near the Kepler frequency Ω(K) while the instability is active above ～0.92 Ω(K) and for temperatures ～(10(9)-2×10(10)) K, characteristic of newborn neutron stars.