Anomalous monopoles of an interacting boson system

Two anomalous monopoles, one of line shape and the other of disk shape, are found to exist in the semiclassical theory of a two-mode interacting boson system. This is in stark contrast with the quantum theory of this system, where only point-like monopoles exist. We show that these two anomalous monopoles have different origins. The line-shaped monopole is formed from the merging of a series of point-like monopoles while the disk-shaped monopole is the result of the collapsing or bundling of field lines of Berry curvature due to the existence of the influence of the interaction between bosons. The relation of these two anomalous monopoles with the famed von Neumann-Wigner theorem is discussed.     

Direct and Indirect Searches for Low-Mass Magnetic Monopoles

Recently, there has been renewed interest in the search for low-mass magnetic monopoles. At the University of Oklahoma we are performing an experiment (Fermilab E882) using material from the old D0 and CDF detectors to set limits on the existence of Dirac monopoles of masses of the order of 500 GeV. To set such limits, estimates must be made of the production rate of such monopoles at the Tevatron collider, and of the binding strength of any such produced monopoles to matter. Here we sketch the still primitive theory of such interactions, and indicate why we believe a credible limit may still be obtained. On the other hand, there have been proposals that the classic Euler–Heisenberg Lagrangian together with duality could be employed to set limits on magnetic monopoles having masses less than 1 TeV, based on virtual, rather than real processes. The D0 collaboration at Fermilab has used such a proposal to set mass limits based on the nonobservation of pairs of photons each with high transverse momentum. We critique the underlying theory, by showing that the cross section violates unitarity at the quoted limits and is unstable with respect to radiative corrections. We therefore believe that no significant limit can be obtained from the current experiments, based on virtual monopole processes.     

Torsional monopoles and torqued geometries in gravity and condensed matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature, and the torsional configurations can be thought of as torsional "monopole" solutions. We explore some of the properties of these configurations in gravity models with a nonvanishing curvature and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.     

Hyperbolic Multi-Monopoles with Arbitrary Mass

On a complete manifold, such as or hyperbolic space , the limit at infinity of the norm of the Higgs field is called the mass of the monopole. We show the existence, on , of monopoles with given magnetic charge and arbitrary mass. Previously, aside from charge one monopoles, existence was known only for monopoles with integral mass (since these arise from U(1) invariant instantons on ). The method of proof is based on Taubes’ gluing procedure, using well-separated, explicit, charge one monopoles. The analysis is carried out in a weighted Sobolev space and necessitates eliminating the possibility of point spectra.     

Brans-Dicke Cosmology with a Scalar Field Dependent Cosmological Term

We propose a cosmology based on the Brans-Dicke theory with a cosmological term dependent in the scalar field. It is shown the existence of a solution in a Robertson-Walker metric that does not suffer from any unnatural fine tuning in the very early Universe such as the horizon, homogeneity, isotropy and flatness problems and does not present any difficulty concerning the GUTs magnetic monopoles.     

Spherical symmetry and magnetic monopoles

I give a general, gauge-invariant, definition of spherical symmetry in a gauge theory. I show that if the fields are required to be non-singular at the origin, such symmetry can occur only for certain values of the magnetic charge. One consequence is the existence of stable monopoles which are not spherically symmetric.     

General relativistic model for energy release of an unstable shell of charged matter in the presence of a dyon core

We construct a formula for the energy released when a spherical shell of charged matter disperses in the presence of a dyon core. Reasons for such a dyon-charged shell configuration on a macroscopic scale stem from the recent speculation concerning the existence of CHAMPS (charged massive particles) along with the possible existence of monopoles produced around the time of nucleosynthesis.     

Monopolium production from photon fusion at the Large Hadron Collider

Magnetic monopoles have attracted the attention of physicists since the founding of the electromagnetic theory. Their search has been a constant endeavor which was intensified when Dirac established the relation between the existence of monopoles and charge quantization. However, these searches have been unsuccessful. We have recently proposed that monopolium, a monopole–antimonopole bound state, so strongly bound that it has a relatively small mass, could be easier to find and become an indirect but clear signature for the existence of magnetic monopoles. Here we extend our previous analysis for its production to two photon fusion at LHC energies.     

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.     

Dual doubled geometry

We probe doubled geometry with dual fundamental branes, i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundamental branes. This dual wrapping rule can be understood by the presence of Kaluza-Klein monopoles. Extending our analysis to supersymmetric solitonic branes with less than or equal to two transverse directions we show that such solitons are precisely obtained by applying the same dual wrapping rule to these cases as well. This extended wrapping rule cannot be explained by the standard Kaluza-Klein monopole alone. Instead, it suggests the existence of a class of generalized Kaluza-Klein monopoles in ten-dimensional string theory.     

Monopole charges in unified gauge theories

Monopole charges, being global quantities, depend on the gauge group of a theory, which in turn is determined by the representations of all its fields. For example, chromodynamics in its present form when combined with electrodynamics has as its gauge group not SU(3) × U(1) but a “smaller” group U(3). The specification of monopole charges for a theory can thus be quite intricate. We report here the result of an investigation in several current gauge theories. Of particular interest is the possible existence in some theories of monopoles carrying multiplicative charges. As a by-product, we clarify some earlier assertions in the literature which seem to us incorrect.     

Liquid-crystal defects and confinement in Yang-Mills theory

It has been shown that, in the Landau gauge of the SU(2) Yang-Mills theory, the residual global symmetry supports the existence of topological vortices which resemble disclination defects in nematic liquid crystals and Alice (half-quantum) vortices in superfluid ³He in the A-phase. The theory also possesses half-integer and integer-charged monopoles, which are analogous to the point-like defects in nematic crystal and in liquid helium. We argue that the deconfinement phase transition in the Yang-Mills theory in the Landau gauge is associated with the proliferation of these vortices and/or monopoles. The text was submitted by the author in English.     

On the Weyl-Wigner-Moyal description of SU (∞) Nahm equations

We show how the reduced self-dual Yang-Mills theory described by the Nahm equations can be carried over to the Weyl-Wigner-Moyal formalism employed recently in self-dual gravity. Evidence of the existence of a correspondence between BPS magnetic monopoles and space-time hyper-Kähler metrics is given.     

Geometrical aspects of magnetic monopoles

The possible topological structures of elementary particles have been investigated to explore the possibility of the existence of magnetic monopoles. It is pointed out that when an elementary charged particle is depicted as an extended body such that the orientation of the internal space (internal helicity) defines the fermion number, the global conservation of this does not allow the existence of a magnetic monopole. Again it is argued that when anisotropy is introduced in the microlocal space-time depicting the internal space of hadrons, this gives rise to the internal symmetry algebra and no non-Abelian gauge fields and Higgs scalars are necessary to have a grand unified scheme of interactions. This avoids theSU ₂ and GUT monopoles. Besides, in this formalism, baryon number corresponds to the orientation or internal helicity of the composite system and the global conservation of this quantum number is found to be a consequence of Lorentz invariance. This forbids the existence of any sort of cosmological monopole in this Lorentz invariant Universe.     

Soliton supermultiplets and Kaluza-Klein theory

We show that the monopoles of five-dimensional Kaluza-Klein theory, considered as solutions of the N = 8 supergravity theory in five dimensions, fit into the same supermultiplets as the original fields in that theory. We show that there is an electric-magnetic duality between these magnetic monopoles and the electrically charged antigravitating objects anticipated by Scherk. We formulate a Bogomolny inequality for N = 8 supergravity, and we speculate on the wider significance of these monopoles.     

Galilean invariance and magnetic monopoles

The existence of Dirac monopoles is shown to be incompatible with Galilean invariance. A discussion follows on the interpretation of monopoles physics in a Galilean approximation.     

Self-dual monopoles in a seven-dimensional gauge theory

The existence of self-dual or anti-self-dual monopoles of a seven-dimensional generalized Yang-Mills-Higgs theory is proved using the second-order equations of motion. The behavior of solutions can be used to recognize self- or anti-self-duality. Moreover, it is shown that, in the class of the field configurations under discussion, the solutions are, in fact, unique.     

Dyons in topological field theories

We examine a class of topological field theories defined by Lagrangians that under certain conditions can be written as the sum of two characteristic numbers or winding numbers. Therefore, the action or the energy is a topological invariant and stable under perturbations. The sufficient conditions required for stability take the form of first-order field equations, analogous to the self-duality and Bogomol'nyi equations in Yang-Mills(-Higgs) theory. Solutions to the first-order equations automatically satisfy the full field equations. We show the existence of nontrivial, nonsingular, minimum energy spherically symmetric dyon solutions and that they are stable. We also discuss evidence for a dual field theory to Yang-Mills-Higgs in topological field theory. The existence of dual field theories and electric monopoles is predicted by Montonen and Olive.     

Magnetic charges,inertia, and arrow of time

The prerelativistic concept of inertial mass (as opposed to gravitational mass) is reconsidered in view of a possible relationship between inertia and magnetic (mass) monopoles. Assuming that such fictitious (topological) charges could have developed in the chaotic early cosmology, a physical principle is suggested, based on dissipation of topological charges and decoupling of interactions, which could have governed the onset of inertia and of the arrow of time, and controlled the critical balance between mass density and expansion rate in the FRW universe. In view of the recent accomplishments in the detection of Dirac monopoles, a generalization of the Eötvos experiment is proposed which could shed light on the grand unification regime. A comment is given on the issue of relating the psychological and the cosmological arrows of time.