Abelian Magnetic Monopoles Research Articles

Thin-wall monopoles in a false vacuum

We study numerically the existence in a false vacuum of magnetic monopoles that are “thin walled,” i.e., which correspond to a spherical region of radius R that is essentially trivial surrounded by a wall of thickness Δ≪R, hence the name thin wall, and finally an exterior region that essentially corresponds to a pure Abelian magnetic monopole. Such monopoles were dubbed false monopoles and can occur in non-Abelian gauge theories where the symmetry-broken vacuum is actually the false vacuum. This idea was first proposed in Kumar []; however, the proof of the existence of thin-wall, false monopoles given there was incorrect. Here, we fill this lacuna and demonstrate numerically, for an appropriately modified potential, the existence of thin-wall false monopoles. The decay via quantum tunneling of the false monopoles could be of importance to cosmological scenarios that entertain epochs in which the Universe is trapped in a symmetry-broken false vacuum. Published by the American Physical Society 2024

Dipole-like Field Configurations in Nonperturbative Vacuum

A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations existing in this theory. Using an assumption of the behavior of the number density of dipole-like field configurations whose energy approaches infinity, we derive an approximate expression for the energy density of such nonperturbative vacuum symmetrical under translation that turns out to be finite, unlike the infinite energy density of perturbative vacuum. Using characteristic values of the parameters appearing in the expression for the nonperturbative energy density, it is shown that this density may be of the order of the energy density associated with Einstein’s cosmological constant. The physical interpretation of the spinor field self-coupling constant as a characteristic distance between dipole-like field configurations is suggested. The questions of experimental verification of the nonperturbative vacuum model under consideration and of determining its pressure are briefly discussed.

Electroweak monopoles and their stability

We apply a generalized field ansatz to describe the spherically symmetric sector of classical solutions in the electroweak theory. This sector contains Abelian magnetic monopoles labeled by their magnetic charge n=±1,±2,…, the non-Abelian monopole for n=±2 found previously by Cho and Maison (CM), and also the electric oscillating solutions. All magnetic monopoles have infinite energy. We analyze their perturbative stability and use the method of complex spacetime tetrad to separate variables and reduce the perturbation equations to multi-channel Schroedinger-type eigenvalue problems. The spectra of perturbations around the CM monopole do not contain negative modes, hence this solution is stable. The n=±1 Abelian monopole is also stable, but all monopoles with |n|≥2 are unstable with respect to perturbations with angular momentum j=|n|/2−1. The Abelian |n|=2 monopole is unstable only within the j=0 sector whereas the CM monopole also has |n|=2 and belongs to the same sector, hence it may be viewed as a stable remnant of the decay of the Abelian monopole. One may similarly conjecture that stable remnants exist also for monopoles with |n|>2, hence the CM monopole is just the first member of a sequence of non-Abelian monopoles with higher magnetic charges. Only the CM monopole is spherically symmetric while all non-Abelian monopoles with |n|>2 are not rotationally invariant.

Constructing the quantum Hall system on the Grassmannians Gr2(CN)

In this talk, we give the formulation of Quantum Hall Effects (QHEs) on the complex Grassmann manifolds Gr2(CN). We set up the Landau problem in Gr2(CN), solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the SU(N) Wigner D-functions for charged particles on Gr2(CN) under the influence of abelian and non-abelian background magnetic monopoles or a combination of these thereof. For the simplest case of Gr2(C4) we provide explicit constructions of the single and many- particle wavefunctions by introducing the Plucker coordinates and show by calculating the two-point correlation function that the lowest Landau level (LLL) at filling factor v = 1 forms an incompressible fluid. Finally, we heuristically identify a relation between the U(1) Hall effect on Gr2(C4) and the Hall effect on the odd sphere S5, which is yet to be investigated in detail, by appealing to the already known analogous relations between the Hall effects on CP3 and CP7 and those on the spheres S4 and S8, respectively. The talk is given by S. Kürkçüoğlu at the Group 30 meeting at Ghent University, Ghent, Belgium in July 2014 and based on the article by F.Ballı, A.Behtash, S. Kürkçüoğlu, G.Ünal [1].

Quantum Hall effect on the GrassmanniansGr2(CN)

Quantum Hall effects on the complex Grassmann manifolds ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ are formulated. We set up the Landau problem in ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ and solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the $SU(N)$ Wigner $\mathcal{D}$ functions for charged particles on ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ under the influence of Abelian and non-Abelian background magnetic monopoles or a combination of these. In particular, for the simplest case of ${\mathbf{Gr}}_{2}({\mathbb{C}}^{4})$, we explicitly write down the $U(1)$ background gauge field as well as the single- and many-particle eigenstates by introducing the Pl\"ucker coordinates and show by calculating the two-point correlation function that the lowest Landau level at filling factor $\ensuremath{\nu}=1$ forms an incompressible fluid. Our results are in agreement with the previous results in the literature for the quantum Hall effect on $\mathbb{C}{P}^{N}$ and generalize them to all ${\mathbf{Gr}}_{2}({\mathbb{C}}^{N})$ in a suitable manner. Finally, we heuristically identify a relation between the $U(1)$ Hall effect on ${\mathbf{Gr}}_{2}({\mathbb{C}}^{4})$ and the Hall effect on the odd sphere ${S}^{5}$, which is yet to be investigated in detail, by appealing to the already-known analogous relations between the Hall effects on $\mathbb{C}{P}^{3}$ and $\mathbb{C}{P}^{7}$ and those on the spheres ${S}^{4}$ and ${S}^{8}$, respectively.

Non-Abelian dual superconductor picture for quark confinement

We give a theoretical framework for defining and extracting non-Abelian magnetic monopoles in a gauge-invariant way in SU(N) Yang-Mills theory to study quark confinement. Then we give numerical evidences that the non-Abelian magnetic monopole defined in this way gives a dominant contribution to confinement of fundamental quarks in SU(3) Yang-Mills theory, which is in sharp contrast to the SU(2) case in which Abelian magnetic monopoles play the dominant role for quark confinement.

On the effective action of center vortices in continuum Yang-Mills theory

The effective action of sufficiently smooth center vortices in continuum Yang-Mills theory is investigated taking into account some of their basic properties observed in lattice simulations. The obtained action is given by the action of an ideal vortex configuration, which is local on the vortex worldsheet, nonlocal quantum corrections due to virtual gluon exchanges, which can be reliably calculated using perturbation theory, and the contribution of Abelian magnetic monopoles. Smooth center vortices appear to have negative rigidity. This implies that, in agreement with lattice data, in the ground state of the theory center vortices are not regular surfaces.

ABELIAN MAGNETIC MONOPOLES AND TOPOLOGICALLY MASSIVE VECTOR BOSONS IN SCALAR-TENSOR GRAVITY WITH TORSION POTENTIAL

A Lagrangian formulation describing the electromagnetic interaction — mediated by topologically massive vector bosons — between charged, spin-½ fermions with an Abelian magnetic monopole in a curved space–time with nonminimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved space–time with isotropic dilaton field, the classical field theory describing the nonrelativistic electromagnetic interaction between a point-like electric charge and magnetic monopole is inconsistent.

Magnetic monopoles in the high temperature phase of Yang–Mills theories

We investigate the properties of thermal Abelian magnetic monopoles in the high temperature phase of Yang–Mills theories, following a recent proposal for their identification on lattice configurations. The study is done for SU(2) pure gauge theory, for temperatures going up to about 10 times the deconfining temperature and using the Maximal Abelian gauge to perform the Abelian projection. We find that the monopole density has a well defined continuum limit. Its temperature dependence disagrees with a free particle gas prediction and is instead well described by a T 3 / ( log ( T / Λ ) ) α behaviour in all the explored range, with α ∼ 2 and Λ ∼ 100 MeV . Also the study of spatial correlations of thermal monopoles shows the presence of non-trivial interactions among them. Finally, we discuss the gauge dependence of our results, showing that it is significant and that, even within the Maximal Abelian gauge, Gribov copy effects are important.

Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom

Recent progress in understanding the emergence of confinement and other nonperturbative effects in the strong interaction vacuum is reviewed. Special emphasis is placed on the role of different types of collective infrared gluonic degrees of freedom in this respect. After a survey of complementary approaches, models of the QCD vacuum based on center vortices, Abelian magnetic monopoles and topological charge lumps such as instantons, merons and calorons are examined. Both the physical mechanisms governing these models as well as recent lattice studies of the respective degrees of freedom are reviewed.

Nonrelativistic Charged Particle-Magnetic Monopole Scattering in the Global Monopole Background

We analyze the nonrelativistic quantum scattering problem of a charged particle by an Abelian magnetic monopole in the background of a global monopole. In addition to the magnetic and geometric effects, we consider the influence of the electrostatic self-interaction on the charged particle. Moreover, for the specific case where the electrostatic self-interaction becomes attractive, the charged particle-monopole bound system can be formed and the respective energy spectrum is a hydrogen-like one.

Nonrelativistic Scattering Analysis of Charged Particle by a Magnetic Monopole in the Global Monopole Background

We analyze the nonrelativistic quantum scattering problem of a charged particle by an Abelian magnetic monopole in the background of a global monopole. In addition to the magnetic and geometric effects, we consider the influence of the electrostatic self-interaction on the charged particle. Moreover, for the specific case where the electrostatic self-interaction becomes attractive, charged particle-monopole bound system can be formed and the respective energy spectrum is hydrogen-like one.

On Nonexistence of Magnetic Charge in Pure Yang-Mills Theories

We prove that magnetic charge does not exist as a physical observable on the physical Hilbert space of the pure SU(2) gauge theory. The abelian magnetic monopoles seen in lattice simulations are then interpreted as artifacts of gauge fixing. The apparent physical scaling properties of the monopole density in the continuum limit observed on the lattice are attributed to the correct scaling properties of physical objects - magnetic vortices, as first argued by Greensite et. al. We can show that a local gauge transformation of a certain type can " create" abelian monopole-antimonopole pairs along magnetic vortices. This gauge transformation exists in pure SU(N) gauge theory at any $N$.

A non-singular potential for the Dirac monopole

We propose a new vector potential for the Abelian magnetic monopole. The potential is non-singular in the entire region around the monopole. We criticize Wu and Yang's derivation of the Dirac quantization condition, and argue how the condition can be derived for any choice of potential. Unlike the Wu–Yang case where two patches are needed to define the full potential, our potential needs only a single patch.

Abelian monopoles and action density in SU(2) gluodynamics on the lattice

We show that the extended Abelian magnetic monopoles in the Maximal Abelian projection of lattice SU(2) gluodynamics are locally correlated with the magnetic and the electric parts of the SU(2) action density. These correlations are observed in the confined and in the deconfined phases.

Abelian magnetic monopole dominance in quark confinement

We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum Yang-Mills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological non-trivial configuration in the functional integral. We derive a version of the non-Abelian Stokes theorem and use it to estimate the expectation value of the Wilson loop. This clearly exhibits the role played by the magnetic monopole as an origin of the Berry phase in the calculation of the Wilson loop in the manifestly gauge invariant manner. We show that the string tension derived from the diagonal (abelian) Wilson loop in the topological field theory (studied in the previous article) converges to that of the full non-Abelian Wilson loop in the limit of large Wilson loop. Therefore, within the above reformulation of QCD, this result (together with the previous result) completes the proof of quark confinement in QCD based on the criterion of the area law of the full non-Abelian Wilson loop.

Self-Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole

We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the solutions of the Dirac equation limits the possibilities such that conservation of angular momentum is restored. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.

Axially symmetric multisphalerons in Yang-Mills-dilaton theory

We construct sequences of axially symmetric multisphaleron solutions in SU(2) Yang-Mills-dilaton theory. The sequences are labelled by a winding number n > 1. For n = 1 the known sequence of spherically symmetric sphaleron solutions is obtained. The solutions within each sequence are labelled by the number of nodes k of the gauge field functions. The limiting solutions of the sequences correspond to abelian magnetic monopoles with n units of charge and energy E ∝ n.

Cooling, monopoles, and the string tension in SU(2) lattice gauge theory

We investigate local cooling of gauge field configurations in four-dimensional SU (2) lattice gauge theory. After abelian projection, abelian magnetic monopole current is identified in the cooled configurations and is used to compute the string tension. The string tension due to the monopoles is seen to be stable under many cooling steps, reproducing the uncooled result, although only 10–15% of the original monopole current links remain.

Electric-magnetic duality in supersymmetric non-Abelian gauge theories

We demonstrate electric-magnetic duality in N = 1 supersymmetric non-Abelian gauge theories in four dimensions by presenting two different gauge theories (different gauge groups and quark representations) leading to the same non-trivial long distance physics. The quarks and gluons of one theory can be interpreted as solitons (non-Abelian magnetic monopoles) of the elementary fields of the other theory. The weak coupling region of one theory is mapped to a strong coupling region of the other. When one of the theories is Higgsed by an expectation value of a squark, the other theory is confined. Massless glueballs, baryons and Abelian magnetic monopoles in the confining description are the weakly coupled elementary quarks (i.e. solitons of the confined quarks) in the dual Higgs description.