Narrow Results

In this paper, we address a theoretical investigation of the gravitational lensing phenomenon within the space-time framework of a holonomy-corrected spherically symmetric black hole (BH), incorporating both ordinary and phantom global monopoles. Our focus lies on the analysis of null geodesics within this BH background, examining the influence of ordinary and phantom global monopoles on the effective potential of null geodesics of the system. Afterwards, we derive analytical expressions for the deflection angle of photon light, considering weak field limit. The obtain expressions are presented up to the second order of the Loop Quantum Gravity parameter, enabling a thorough examination of the impact of ordinary and phantom global monopoles on the deflection angle.

In this analysis, we analytically obtain the eigenvalue solutions of non-relativistic quantum particles interacting with Mie-type potential in a topological defect geometry. Afterward, we study the thermodynamic properties for the quantum system, such as the vibrational free energy, mean energy, entropy, and specific heat using the partition unction and analyze the effects of topological defect. Furthermore, we calculated the Shannon entropy for this quantum system, thus measuring the loss of information about the particle’s location. This measure of information reveals the influence of the topological parameter on the location of the particle and provides us with more detailed parameters for a possible experimental detection of these quantum particles.

The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, non-smooth Runge–Lenz vector can exist; there is, however, a spectrum-generating conformal o(2,1) dynamical symmetry that extends into osp(1/1) or osp(1/2) for spin 1/2 particles. Self-dual 't Hooft–Polyakov-type monopoles admit an su(2/2) dynamical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin 0 case. For large r, the system reduces to a Dirac monopole plus a suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the "dyon" of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a "helicity-supersymmetry" analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza–Klein monopole of Gross–Perry–Sorkin. For the magnetic vortex, the N = 2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the o(2) × o(2,1) bosonic symmetry into an o(2) × osp(1/2) dynamical superalgebra.

Magnetic monopole currents are believed to have a strong impact on the Monte Carlo dynamics of compact quantum electrodynamics near the phase transition. We have indications that updating algorithms have to form and to break up monopole current clusters in order to force the tunneling of the system between the coexisting phases, the confined phase and the Coulomb phase. This might be responsible for long lived metastabilities in the time series.

We present parallel numerical algorithms which allow the fast identification of clusters of monopole loops, the determination of their topological properties as well as their visualization in the course of a Monte Carlo simulation. The algorithms are implemented on the Connection Machine CM-5. We compare the data parallel programming style with a message passing approach. Complexity and performance are discussed.

(2 + 1)-dimensional Georgi–Glashow model is explored in the regime when the Higgs boson is not infinitely heavy, but its mass is of the same order of magnitude as the mass of the W-boson. In the weak-coupling limit, the Debye mass of the dual photon and the expression for the monopole potential are found. The cumulant expansion applied to the average over the Higgs field is checked to be convergent for the known data on the monopole fugacity. These results are further generalized to the SU(N)-case. In particular, it is found that the requirement of convergence of the cumulant expansion establishes a certain upper bound on the number of colors. This bound, expressed in terms of the parameter of the weak-coupling approximation, allows the number of colors to be large enough. Finally, the string tension and the coupling constant of the so-called rigidity term of the confining string are found at arbitrary number of colors.

An attempt has been made to analyze the magnetic symmetry of the non-Abelian gauge theory associated with the strong interactions using the fibre bundle formulation. Utilizing the gauge field topology, the analysis of dual dynamics associated with the non-Abelian fields is shown to have important bearings on the nonperturbative hadronic effects like confinement of colored quarks and gluons inside hadrons. The state of dual superconductivity for the magnetically condensed vacuum has been analyzed to understand the bulk QCD magnetic properties by evaluating the current correlators in magnetic gauge in terms of the dielectric parameters. The dielectric behavior has been shown to lead to the p^-4 confining nature to the dual gluon propagators and to provide an effective macroscopic description of the complicated nonperturbative microscopic interactions of charged particles in dual QCD. The p^-4 behavior of dual gluon propagator has also been shown to confirm the linearly rising inter-quark confining potential with an explicit dual gluon mass dependency in dual QCD.

The RG flow in the finite-temperature (2 + 1)D Georgi–Glashow model is explored in the regime when the Higgs field is not infinitely heavy, but its mass is rather of the same order of magnitude as the mass of the W-boson. The corrections to the standard RG flow are derived to the leading order in the inverse mass of the Higgs boson. The scaling of the free-energy density in the critical region and the value of the critical temperature of the Berezinsky–Kosterlitz–Thouless (BKT) phase transition are found to be unaffected by the finiteness of the Higgs–boson mass. The evolution of the Higgs mass itself is also investigated and shown to be rather weak, that enables one to treat this parameter as a constant. The same analysis is further performed in the SU(N)-case at N > 2, where the RG invariance is demonstrated to hold only approximately, in a certain sense. Modulo this approximation, the critical behavior of the SU(N)-model turns out to be identical to that of the SU(2)-one.

We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting from the two-center McIntosh–Cisneros–Zwanziger (MICZ)–Kepler system and making the reduction into these two-dimensional surfaces, we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the same two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

In this paper, we investigate the behavior of a scalar bosonic field within the backdrop of Eddington-inspired Born–Infeld gravity with a global monopole configuration. Additionally, we consider the presence of both scalar and vector potentials. To introduce the scalar potential, we perform a transformation on the mass term, replacing $M^2$ with ${(M+S)}^2$. For the vector potential, we apply a minimal coupling scheme, transforming $p_{\mu }\to D_{\mu }\equiv (p_{\mu }-e{A}_{\mu })$ within the relativistic Klein–Gordon equation. We opt for a harmonic oscillator scenario where the scalar and vector potentials are equal, i.e. $S=V\propto x^2$. Through this setup, we analytically solve the wave equation using the confluent Heun equation form. Subsequently, we delve into the quantum system in the absence of any potential, determining the permissible values for bound-state relativistic energy levels and the scalar field’s wave function. Our analysis reveals that the energy levels and wave function are influenced by various parameters present in the eigenvalue expression.

The asymmetry, between electric (E) and magnetic (H) fields of Maxwell's equation is here analyzed by using the concept of chirality. The chiral spinorial approach sets the stage for the construction of a more general theory of spin-1 particles than usual electrodynamics. Chiral components of a rank-2 spinor field are taken as the dynamic variables of the theory. A rank-2 spinor accommodates another particle (the magnetic photon). This new particle emerges naturally from chiral invariance arguments. The nonexistence, in nature, of such a particle is the reason for the nonexistence of monopoles and the asymmetry in Maxwell's equation. The existence of magnetic monopoles would restore the symmetry of Maxwell's equation. We establish, in this way, at a very formal level, the connection between magnetic monopoles and chiral asymmetry.

We argue that there are no axially symmetric rotating monopole solutions for a Yang–Mills–Higgs theory in flat space–time background. We construct axially symmetric Yang–Mills–Higgs solutions in the presence of a negative cosmological constant, carrying magnetic charge n and a nonvanishing electric charge. However, these solution are also nonrotating.

We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole positions. We find periodic deviations from the 1/r-behavior of the monopole-antimonopole potential leading to local extrema. We suppose that these meta-stabilities may influence the order of the phase transition in compact QED.

Earlier investigations [Int. J. Mod. Phys. A19, 5017 (2004)] showed local minima in the monopole–antimonopole potential in U(1) gauge theory on the lattice. In this paper we localize monopoles of Monte Carlo configurations. A statistical analysis of localization measurements gives us the probability density which we compare with the potential found in Ref. 1. We find the monopoles mainly located either in the center of three-dimensional cubes or on the interface between two cubes. This agrees with the position of minima and maxima of the monopole–antimonopole potential.

It has been suggested that superheavy charged particles might have been born in primordial bound pairs at the end of cosmic inflation. Such pairs have been proposed as a source of ultrahigh energy cosmic rays (UHECR). We show that primordial bound pairs of magnetic monopoles larger than 10^-9 cm quickly thermalise due to the interaction with primordial electron–positron plasma and any such initial primordial concentration is washed out. The final concentration will therefore be defined by their equilibrium abundance.

A Monopole–Antimonopole pair could annihilate producing a photon shower: Some aspects of the shower like the multiplicity distribution and angular correlations are investigated within a model suitable for processes with high multiplicities and therefore difficult to deal with standard perturbative treatment. The possible production of electron–positron pairs is also considered.

The radiation of photons by a colliding monopole–antimonopole pair is studied. The process is described in terms of classical trajectories for the incoming pair and quantized field for the produced particles. The investigation is performed in order to complete a previous one, where the monopole–antimonopole pair formed a bound state.

The production of a monopole–antimonopole pair through electromagnetic interaction is considered. The particular process considered involves the annihilation of a pair of leptons into photons and the subsequent formation of the MA pair. The actual calculation involves some approximations but no expansion in coupling constant.

In this review, we discuss recent developments in both the theory and the experimental searches of magnetic monopoles in past, current and future colliders and in the Cosmos. The theoretical models include, apart from the standard Grand Unified Theories, extensions of the Standard Model that admit magnetic monopole solutions with finite energy and masses that can be as light as a few TeV. Specifically, we discuss, among other scenarios, modified Cho–Maison monopoles and magnetic monopoles in (string-inspired, higher derivative) Born–Infeld extensions of the hypercharge sector of the Standard Model. We also outline the conditions for which effective field theories describing the interaction of monopoles with photons are valid and can be used for result interpretation in monopole production at colliders. The experimental part of the review focuses on, past and present, cosmic and collider searches, including the latest bounds on monopole masses and magnetic charges by the ATLAS and MoEDAL experiments at the LHC, as well as prospects for future searches.

The production of pairs of monopole–antimonopole in presence of extremely intense magnetic fields, is briefly investigated in the case where the magnetic field undergoes also a time variation. The possibility that similar conditions are realized, with a production of ordinary particles, was already considered for astrophysical phenomena, e.g. some phases of evolution of neutron stars.

A possible indirect way of detecting the presence of a monopole would be the detection of a photon shower originating from a collision of a monopole with an ordinary particle in the atmosphere with the accompanying Bremsstrahlung. Since a similar photon production can be interpreted as Bremsstrahlung by a heavy nucleus the observation of the simultaneous production of electron–positron pairs may help in distinguishing the two cases.