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The uniqueness of axisymmetric monopole solutions to the Bogomolny equations is studied. The generalized Green identity for harmonic maps is used to prove that the Prasad-Sommerfield solution is the unique axisymmetric one-monopole solution. The multimonopole solutions are also discussed.
It is found that the effective Hamiltonian for nuclear rotation in a diatom is equivalent to that of a charged particle in a background magnetic-monopole field. In certain cases, half-integer orbital angular momentum or non-Abelian fields occur. Furthermore, the effects of magnetic-monopole-like gauge fields can be experimentally observed in spin-resonance experiments with variable magnetic fields.
The Parker bound on the flux of magnetic monopoles is extended and strengthened. A new limit on the survival and growth of a small galactic seed field is obtained which rules out the possibility that monopoles much lighter than 10 exp 17 GeV/sq c can provide the closure density of the universe.
Farassat's formulations provide an acoustic prediction at an observer location provided a source surface, including motion and flow conditions. This paper presents compact forms for the monopole term of several of Farassat's formulations. When the physical surface is elongated, such as the case of a high aspect ratio rotorcraft blade, compact forms can be derived which are shown to be a function of the blade cross sectional area by reducing the computation from a surface integral to a line integral. The compact forms of all formulations are applied to two example cases: a short span wing with constant airfoil cross section moving at three forward flight Mach numbers and a rotor at two advance ratios. Acoustic pressure time histories and power spectral densities of monopole noise predicted from the compact forms of all the formulations at several observer positions are shown to compare very closely to the predictions from their non-compact counterparts. A study on the influence of rotorcraft blade shape on the high frequency portion of the power spectral density shows that there is a direct correlation between the aspect ratio of the airfoil and the error incurred by using the compact form. Finally, a prediction of pressure gradient from the non-compact and compact forms of the thickness term of Formulation G1A shows that using the compact forms results in a 99.6% improvement in computation time, which will be critical when noise is incorporated into a design environment.
Recently there has developed a renewed interest in the ionization losses of slow monopoles. An excellent summary of the literature is contained in a paper of Ahlen and Kinoshital (hereafter referred to as A.K.). A.K. have derived lower bounds for the ionization losses of a slow monopole passing through matter. However, they neglected the effects of an energy gap, in insulating materials, on the excitation of atomic electrons. Using the Thomas-Fermi statistical model of atomic wave functions, we have calculated lower bounds for ionization losses in "insulators" including effects due to an energy gap. The Fermi-Teller theory 2 (hereafter referred-to as F.T.) was originally used to predict the stopping, by ionization losses, of slow charged particles in materials. The theory is based on a calculation of the energy lost to a uniform "Fermi sea". However, the authors note that the actual "Fermi velocity" cancels out in the derivation. Therefore their calculated results also apply to a "Thomas-Fermi" atom, in which each volume element is considered to be a Fermi sea filled to the top of the potential well with atomic electrons.
Monopole-antimonopole pair dyons are presented. The dyons possess opposite magnetic charge but carry the same electric charge. These stationary dyons possess finite energy. However they do not satisfy the first order Bogomol'nyi equations and are non-BPS solutions. They are axially symmetric and are characterized by a parameter, -1{<=}{eta}{<=}1 which determines the net electric charges of these dyons. These dyon solutions are solved numerically when the magnetic charge of the dipoles are n = {+-}1, {+-}2 for both vanishing and non-vanishing strength of the Higgs field potential. When {lambda} = 0, the dipole separation, total energy and net electric charge of the dyons increase exponentially fast to infinity when {eta} approaches {+-}1. However, when {lambda} = 1, all these three quantities approach finite critical values as {eta} approaches {+-}1.
We show that the non-Abelian magnetic monopole defined in a gauge-invariant way in SU(3) Yang-Mills theory gives a dominant contribution to confinement of the fundamental quark, in sharp contrast to the SU(2) case.
In this work, we describe degenerate square spin as an ensemble of magnetic monopoles coupled via an emergent entropic field that subsumes the effect of the underlying spin vacuum. We compute their effective free energy, entropic interaction, correlations, screening, and structure factor, and find that they coincide with the experimental ones. Unlike in pyrochlore ices, a dimensional mismatch between real and entropic interactions leads to weak singularities at the pinch points and algebraic correlations at long distances. This algebraic screening can be, however, camouflaged by a pseudoscreening regime.
A magnetic-monopole solution of a non-Abelian gauge theory as proposed by 't Hooft and Polyakov is studied in the Vaidya space-time. We find that the solutions of Einstein equations generates a geometry of the Bonnor-Vaidya space-time corresponding to magnetically charged null fluid with Higgs field contributing a cosmological term. In the absence of the scalar fields the corresponding Wu-Yang solution of the gauge theory still generates the Bonnor-Vaidya geometry, but with no cosmological term.
We investigate the validity of the Dirac quantization condition for magnetic monopoles in noncommutative space-time. We use an approach which is based on an extension of the method introduced by Wu and Yang. To study the effects of noncommutativity of space-time, we consider the gauge transformations of U{sub *}(1) gauge fields and use the corresponding deformed Maxwell's equations. Using a perturbation expansion in the noncommutativity parameter {theta}, we show that the Dirac quantization condition remains unmodified up to the first order in the expansion parameter. The result is obtained for a class of noncommutative source terms, which reduce to the Dirac delta function in the commutative limit.
We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.
Here, we discuss the non-Abelian artificial magnetic monopoles associated with n-level energy crossing in quantum systems. We found that hidden symmetries reveal themselves as observables such as spin, hypercharge, and other physical degrees of freedom. We illustrated our results on concrete examples of two and three energy-level crossings. Our findings can be helpful for modeling various phenomena in physical systems such as SU(N) topological insulators and spintronic devices based on topological insulators.
In the Landau problem on the two-dimensional plane, physical displacement of a charged particle (i.e., magnetic translation) can be induced by an in-plane electric field. The geometric phase accompanying such magnetic translation around a closed path differs from the topological phase of Aharonov and Bohm in two essential aspects: The particle is in direct contact with the magnetic field and the geometric phase has an opposite sign from the Aharonov–Bohm phase. We show that magnetic translation on the two-dimensional cylinder implemented by the Schrödinger time evolution truly leads to the Aharonov–Bohm effect. The magnetic field normal to the cylinder’s surface corresponds to a line of magnetic monopoles of uniform density whose simulation is currently under investigation in cold atom physics. In order to characterize the quantum problem, one needs to specify the value of the magnetic flux (modulo the flux unit) that threads but not in touch with the cylinder. A general closed path on the cylinder may enclose both the Aharonov–Bohm flux and the local magnetic field that is in direct contact with the charged particle. This suggests an extension of the Aharonov–Bohm experiment that naturally takes into account both the geometric phase due to local interaction with the magnetic field and the topological phase of Aharonov and Bohm.
The structure of exotic nuclei around N = 28 is investigated in the sd-pf shell-model space using a new effective interaction. The cross-shell part of the interaction is provided by the monopole-based universal interaction which has been successful in accounting for single-particle evolution in several mass regions. Focusing on the nuclear structure that is sensitive to the shell evolution, we show successful results for the proton-hole states in K isotopes and large deformation in {sup 42}Si. The results demonstrate that the present scheme may be a promising way for constructing an effective interaction for other mass regions.
We present recent results on quark confinement: in SU(3) Yang-Mills theory, confinement of fundamental quarks is obtained due to the dual Meissner effect originated from non-Abelian magnetic monopoles defined in a gauge-invariant way, which is distinct from the well-known Abelian projection scenario. This is achieved by using a non-Abelian Stokes theorem for the Wilson loop operator and a new reformulation of the Yang-Mills theory.
We present a systematic approach to the linearized Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral properties. We show that a quaternionic formulation allows for a compact and efficient treatment of the linearized equations in the Bogomol'nyi-Prasad-Sommerfield limit of vanishing Higgs self-coupling and use it to study both scattering and bound states. We focus on the sector of vanishing generalized angular momentum and analyze it numerically, putting zero-energy bound states, Coulomb bound states, and infinitely many Feshbach resonances into a coherent picture. We also consider the linearized Yang-Mills-Higgs equations with nonvanishing Higgs self-coupling and confirm the occurrence of Feshbach resonances in this situation.
We study Polchinski’s “fermion-rotor system” as an accurate description of charged Weyl fermions scattering on a magnetic monopole core in the limit of zero gauge coupling. Traditionally it was thought such scattering could lead to fractional particle numbers (“semitons”). By direct calculations we show those semitonic processes are in fact free propagation, facilitated by composite fermion-rotor operators interpolating the “forbidden” states, effectively “recovering” both ingoing and outgoing states in every lowest partial wave. Nonsemitonic Callan-Rubakov processes are unchanged.
An approximate expression for the Euclidean Green function of a massless scalar field in the spacetime of a multidimensional global monopole has been derived. Expressions for the vacuum expectation values 〈ϕ{sup 2}〉{sub ren} and 〈T{sub 00}〉{sub ren} have been derived by the dimensional regularization method. Comparison with the results obtained by alternative regularization methods is made.