Monopole Field Research Articles

Cartan monopoles

The effective Hamiltonians for chiral supersymmetric gauge theories at small spatial volume are generalizations of the Hamiltonians describing the motion of a scalar or a spinor particle in a field of Dirac monopoles (we are dealing in fact with a certain lattice of monopoles supplemented with a periodic singular potential). The gauge fields in such Hamiltonians belong to the Cartan subalgebras of the corresponding gauge algebras. Such a construction exists for all groups admitting complex representations, i.e., for SU(N≥3), Spin(4n+2) with n≥1 and E6. We give explicit expressions for these Hamiltonians for SU(3), SU(4)≃Spin(6) and for SU(5). The simplified version of such a Hamiltonian, deprived of fermion terms, of the extra scalar potential and when only one node of the lattice is taken into consideration, describe a 3r-dimensional motion (r being the rank of the group) in the field what we call a “Cartan monopole.” As is the case for the ordinary monopole, the Lagrangian of this system enjoys gauge symmetry, rotational symmetry, and the parameter, generalizing the notion of magnetic charge for Cartan monopoles, is quantized. Published by the American Physical Society 2024

Gauge formulation for magnetic monopoles from generalized gauge fields

In this work, we propose an alternative path to establish a gauge theory for magnetic monopoles. The approach involves a simple improvement of the original formulation by Dirac and is based on utilizing non-global potentials associated with Dirac strings. In the present case, we adopt the concept of generalized vector fields to build up generalized gauge potentials for the electromagnetic fields. The main advantage is to work with just one single global (generalized) vector potential to describe the monopole field throughout the entire space, except at the point where the monopole is located, rather than adopting multi-valued functions. We argue that the treatment presented in this paper also leads to electric charge quantization, similar to the case with the Dirac monopoles. We discuss the point-like source associated with the monopole we hope it could be helpful for the search of magnetic monopoles in the laboratory.

Engineering and revealing Dirac strings in spinor condensates

Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and show that there exists a mapping between the vortex filament and the Dirac string. We also devise a proposal where preparing initial spin states with relevant symmetries can result in different vortex patterns, revealing an underlying correspondence between the internal spin states and the spherical vortex structures. Such a mapping also leads to a new way of constructing spherical Landau levels, and monopole harmonics. Our observation provides insights into the behavior of quantum matter possessing internal symmetries in curved spaces. Published by the American Physical Society 2024

Effective Abelian lattice gauge field theories for scalar-matter-monopole interactions

We present a gauge and Lorentz invariant effective field theory model for the interaction of a charged scalar matter field with a magnetic monopole source, described by an external magnetic current. The quantum fluctuations of the monopole field are described effectively by a strongly coupled “dual” Ud(1) gauge field, which is independent of the electromagnetic Uem(1) gauge field. The effective interactions of the charged matter with the monopole source are described by a gauge invariant mixed Chern-Simons-like (Pontryagin-density) term between the two U(1) gauge fields. The latter interaction coupling is left free, and a lattice study of the system is performed with the aim of determining the phase structure of this effective theory. Our study shows that, in the spontaneously broken-symmetry phase, the monopole source triggers, via the mixed Chern-Simons term, which is nontrivial in its presence, the generation of a dynamical singular configuration (magnetic-monopolelike) for the respective gauge fields. The scalar field also behaves in the broken phase in a way similar to that of the scalar sector of the ’t Hooft-Polyakov monopole. Moreover, we show that the modest size of the lattices involved does not have significant effects on the main conclusions of our analysis. Published by the American Physical Society 2024

Current Sheet Alignment in Oblique Black Hole Magnetospheres: A Black Hole Pulsar?

We study the magnetospheric evolution of a nonaccreting spinning black hole (BH) with an initially inclined split monopole magnetic field by means of 3D general relativistic magnetohydrodynamic simulations. This serves as a model for a neutron star (NS) collapse or a BH–NS merger remnant after the inherited magnetosphere has settled into a split monopole field creating a striped wind. We show that the initially inclined split monopolar current sheet aligns over time with the BH equatorial plane. The inclination angle evolves exponentially toward alignment, with an alignment timescale that is inversely proportional to the square of the BH angular velocity, where higher spin results in faster alignment. Furthermore, magnetic reconnection in the current sheet leads to exponential decay of event-horizon-penetrating magnetic flux with nearly the same timescale for all considered BH spins. In addition, we present relations for the BH mass and spin in terms of the period and alignment timescale of the striped wind. The explored scenario of a rotating, aligning, and reconnecting current sheet can potentially lead to multimessenger electromagnetic counterparts to a gravitational-wave event due to the acceleration of particles powering high-energy radiation, plasmoid mergers resulting in coherent radio signals, and pulsating emission due to the initial misalignment of the BH magnetosphere.

Newton's Off-Center Circular Orbits and the Magnetic Monopole

Introducing a radially dependent magnetic field into Newton's off-center circular orbits potential so as to preserve the $E=0$ dynamical symmetry leads to a unique choice of field that can be identified as the inclusion of a magnetic monopole in the inverse stereographically projected problem. One finds also a phenomenological correspondence with that of the linearly damped Kepler model. The presence of the monopole field deforms the symmetry algebra by a central extension, and the quantum mechanical version of this algebra reveals a number of zero modes equal to that counted using the index theorem of elliptic operators.

Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles

We consider an Einstein-scalar field model which is a consistent truncation of mathcal{N} = 8 D = 4 gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic selfinteraction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.

On magnetic monopole and Dirac quantization condition in the minimal length formalism

In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field, we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent on the deformation parameter α. In addition, we find that the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple; thus, we establish that the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α. The modified Dirac quantization condition allows fractional charges that arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross-section and then we estimate the upper bound on the minimal length.

Regular Electric Field in Electromagnetic Coupled to a Scalar Field

AbstractIn the framework of an electromagnetic field coupled nonminimally with a scalar field in flat spacetime, the existence of a non‐singular electric field is proved for a point electric charge or electric monopole. In analogy with the Maxwell‐dilaton system introduced by Gibbons and Wells, first, a Maxwell‐anti‐dilaton system is constructed where the radial electric field of a static electric monopole is coupled to an anti‐dilaton. The field equations are solved analytically for the electric and dilaton fields and observe the nonsingular electric field. Also, the self‐energy of the electric monopole is found to be finite. Furthermore, the formalism to a Maxwell‐scalar field is generalized where a mechanism is introduced upon which the coupled regular‐electric field and scalar field is obtained. The formalism shows that for a given regular electric field there are two supersymmetric coupling functions corresponding to a scalar and a phantom field.

Momentum: QFT, Quantum Black Holes, and Some Cosmological Implications

The paper studies the general Pauli-like equation for a Dirac fermions doublet on the background of an external non-Abelian monopole field. The variables separation has been fulfilled, the non-relativistic approximation for the radial systems has been derived. For the case of a minimal value of the conserved quantum number j = 0, the Pauli equation has been obtained in the form of one second-order differential equation. In the case j > 0, the problem has been reduced to the system of two coupled second order equations. In Bogomol'nyi-Prasad-Sommerfeld approximation, this system of equations has been solved in terms of hypergeometric functions.

Decomposition of the SU(2) gauge field in the maximal Abelian gauge

We study decomposition of $SU(2)$ gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge in $SU(2)$ lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the static potential due to the modified nonabelian field describes the string fluctuations energy.

Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem

The light trajectory in the gravitational field of one body at rest with monopole and quadrupole structure is determined in the second post-Newtonian (2PN) approximation. The terms in the geodesic equation for light rays are separated into time-independent tensorial coefficients and four kind of time-dependent scalar functions. Accordingly, the first and second integration of geodesic equation can be reduced in each case to only four kind of scalar master integrals. These integrals can be solved in closed form by recurrence relations. The 2PN terms of monopole and quadrupole contribute less than $1$ nano-arcsecond to the total light deflection. There are, however, enhanced terms in the 2PN light deflection, both in case of monopole and quadrupole. These enhanced 2PN terms are caused by the use of an impact vector which is indispensable for modeling of real astrometric measurements. In case of grazing light rays at Jupiter and Saturn, the enhanced 2PN terms, caused by the quadrupole structure of the body, amount up to 0.95 micro-arcseconds and 0.29 micro-arcseconds, respectively. Thus, the 2PN quadrupole terms are relevant for high-precision astrometry on the sub-micro-arcsecond scale of accuracy.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

Conformal bridge transformation and symmetry

The conformal bridge transformation (CBT) is reviewed in the light of the symmetry. Originally, the CBT was presented as a non-unitary transformation (a complex canonical transformation in the classical case) that relates two different forms of dynamics in the sense of Dirac. Namely, it maps the asymptotically free form into the harmonically confined form of dynamics associated with the conformal symmetry. However, as the transformation relates the non-Hermitian operator , where is the generator of dilations, with the compact Hermitian generator of the algebra, the CBT generator can be associated with a -symmetric metric. In this work we review the applications of this transformation for one- and two-dimensional systems, as well as for systems on a cosmic string background, and for a conformally extended charged particle in the field of Dirac monopole. We also compare and unify the CBT with the Darboux transformation. The latter is used to construct -symmetric solutions of the equations of the KdV hierarchy with the properties of extreme waves. As a new result, by using a modified CBT we relate the one-dimensional -regularized asymptotically free conformal mechanics model with the -regularized version of the de Alfaro, Fubini and Furlan system.

Proximity resonances of water-entrained air bubbles near acoustically reflecting boundaries.

The acoustic resonances of radiatively damped air bubbles in water near reflecting boundaries are investigated by representing the bubble and its image by two bubbles in a full space, ensonified by two incident fields. Results obtained using an analytic monopole theory are compared with those of a coupled spherical harmonic technique and a boundary element method. Near a rigid boundary, the resonance frequency is reduced, and the response characteristics are determined by the predominant monopolar character of the individual bubble motion, with small changes in peak amplitude and Q. Near a sound-soft boundary, a higher frequency proximity resonance is observed. The monopole field is cancelled out, and the response is determined by higher-order scattering modes, giving very high values of Q. While the individual bubble scattering level increases significantly, the overall scattering is less than for two uncoupled bubbles. For bubble separations of 8-28 radii, all three approaches predict essentially identical results for both boundary types. For bubble separations less than one radius, the monopole theory, which does not include higher-order scattering modes, diverges from the boundary element and coupled spherical harmonic methods, whose high-accuracy determinations of resonance frequencies and amplitudes agree to within 0.1%.

Astrophysical quantum matter: spinless charged particles on a magnetic dipole sphere

We consider the quantum mechanics of a spinless charged particle on a 2-dimensional sphere. When threaded with a magnetic monopole field, this is the well-known Haldane sphere that furnishes a translationally-invariant, incompressible quantum fluid state of a gas of electrons confined to the sphere. This letter presents the results of a novel variant of the Haldane solution where the monopole field is replaced by that of a dipole. We argue that this system is relevant to the physics on the surface of compact astrophysical objects like neutron stars.

Generalized spinning particles on {mathcal {S}}^2 in accord with the Bianchi classification

Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on {mathcal {S}}^2, the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar models, which rely upon real Lie algebras with dimensions d=4,5,6, is elucidated.

Deflection light in strong field from global monopole in Eddington-inspired Born-Infeld gravity

We examine the deflection of light due to the gravitational field of global monopole in Eddington-inspired Born-Infeld theory using strong field approach, which accurately explains light deflection when the impact parameter is small. In this paper, we will discuss the deflection angle and the radius of the photon sphere. We discover that the global monopole will increase the deflection angle and the radius of the photon sphere (compared to Schwarzschild), while EiBI parameter will decrease the radius of the photon sphere and the decreasing of deflection angle is shown clearly with small impact parameter.

Molecular Impurities as a Realization of Anyons on the Two-Sphere.

Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.

О внутренней геометрии траекторий заряженных частиц в симметричных внешних полях

The curvature and torsion of the trajectories of charges in external gauge fields, including the fields of magnetic monopoles, are calculated. It is shown that these quantities are efficiently calculated using the equations of motion and first integrals. For a wide class of magnetic fields, their form-invariant combination was found.