Narrow Results

We sketch the development of effective theories for SU(2) and SU(3) Yang–Mills thermodynamics. The most important results are quoted and some implications for particle physics and cosmology are discussed.

We consider the production of magnetic monopoles via γγ fusion at high energy pp collisions. In the assumption that the monopole spin is equal 0, 1/2, 1, the monopole–antimonopole pair production cross-section by this mechanism at LHC energies is estimated and analyzed.

Chiral monopoles are hedgehoglike structures in local chiral condensates in QCD. These monopoles are (i) made of quark and gluon fields; (ii) explicitly gauge-invariant; (iii) they carry quantized and conserved chromomagnetic charge. We argue that the chiral condensate vanishes in a core of the chiral monopole while the density of these monopoles increases with temperature wiping out the quark condensate in quark-gluon plasma. We suggest that the chiral monopoles are responsible for the chiral symmetry restoration in QCD. We also argue that the chiral monopoles are unlikely to be responsible for confinement of color. Thus, phenomena of the chiral symmetry restoration and the color deconfinement in QCD are not necessarily related to each other and the corresponding transitions may happen at different temperatures.

It is proposed to extend the nuclear physics by including the magnetic monopole as the additional component. It is indicated that the nuclear reaction of such a system is drastically different from the ordinary nuclear reaction.

An equivalence of total angular momentum operator of charge–monopole system to the momentum operator of a symmetrical quantum top is observed. This explicitly shows the string independence of Dirac's quantization condition leading to disappearance of Schwinger's string and reveals some properties of diatomic molecule for this system.

In 2010, the CERN (European Centre for Particle Physics Research) Research Board unanimously approved MoEDAL, the seventh international experiment at the Large Hadron Collider (LHC), which is designed to search for avatars of new physics signified by highly ionizing particles. A MoEDAL discovery would have revolutionary implications for our understanding of the microcosm, providing insights into such fundamental questions as: do magnetic monopoles exist, are there extra dimensions or new symmetries of nature; what is the mechanism for the generation of mass; what is the nature of dark matter and how did the big bang unfurl at the earliest times.

We have studied the Maxwell–Higgs model on the surface of an infinite cylinder. In particular, we show that this model supports self-dual topological soliton solutions on the infinite tube. Finally, the Bogomol’nyi-type equations are studied from theoretical and numerical point of view.

By using an appropriate transformation, it was shown that the quantum system of four-dimensional (4D) simple harmonic oscillator can describe the motion of a charged particle in the presence of a magnetic monopole field. It was shown that the Dirac magnetic monopole has the hidden algebra of U(1) symmetry and by reducing the dimensions of space, the U(1) × U(1) dynamical group for 4D harmonic oscillator quantum system was obtained. Using the group representation and based on explicit solution of the obtained differential equation, the spectrum of system was calculated.

In this paper, we will explore the spacetime phase structure inside the Infeld–van der Waerden formalisms, showing that Maxwell’s theory in this scenario leads to an axion-like phase electrodynamics, which suggests that this phase may originate the axion field.

For a charge-monopole pair, we have another definition of the orbital angular momentum, and the transverse part of the momentum including the vector potential turns out to be the so-called geometric momentum that is under intensive study recently. For the charge on the spherical surface with the monopole at the origin, the commutation relations between all components of both the geometric momentum and the orbital angular momentum satisfy the so(3,1) algebra. With construction of the geometrically infinitesimal displacement operator based on the geometric momentum, the so(3,1) algebra implies the Aharonov–Bohm phase shift. The related problems such as charge and flux quantization are also addressed.

After having obtained previously an extended first approximation of Maxwell’s equations in Fock’s nonlinear relativity, we propose here the corresponding exact form. In order to achieve this goal, we were inspired mainly by the special relativistic version of Feynman’s proof from which we constructed a formal approach more adapted to the noncommutative algebra. This reasoning lets us establish the exact form of the generalized first group of Maxwell’s equations. To deduce the second one, we have imposed the electric–magnetic duality. As in the k-Minkowski spacetime, the generalized Lorentz force depends on the mass of the particle. After having restored the R-Lorentz algebra symmetry, we have used the perturbative treatment to find the exact form of the generalized Dirac’s magnetic monopole in our context. As consequence, the Universe could locally contain the magnetic charge but in its totality it is still neutral.

There are some particle physics theories that go beyond the so-called “standard cosmological model” to predict the existence of magnetic monopoles (MMs). The discovery of MMs would be an incredible breakthrough in high-energy physics. The existence of MMs in the early Universe has been speculated and anticipated from Grand Unified Theory. If MMs exist, the inverse powers of the unification mass will not suppress the baryon number violating effects of grand unified gauge theories. Therefore, MM catalyzing nucleon decay is a typical strong interaction. This phenomenon is due to the boundary conditions that must be imposed on the core of MM fermion fields. We present a possible mechanism to explain the formation of the Hot Big Bang Cosmology. The main ingredient in our model is nucleon decay catalyzed by MMs (i.e. the Rubakov–Callan effect). It is shown that Hot Big Bang developed naturally because the luminosity due to the Rubakov–Callan effect is much greater than the Eddington luminosity (i.e. $L_m>10^4{L}_{\mathrm{\text{Edd}}}$).

We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy conservation, and the stress-energy tensor. The formalism also enabled us to generalize the Dirac monopole and the charge quantization rule.

In this paper, we mainly focus on 22 old white dwarfs and present two new magnetic monopoles (MMs) energy cooling resources models (I) and (II) based on MMs catalytic nuclear decay. We discussed their luminosity, and compared with the observations. The luminosities for these old White Dwarf stars (WDs) for models (I) and (II) are well in agreement with the observations $L_{\mathrm{\text{rad}}}$ and the differences are no more than one order magnitude at relativistic low temperature (e.g. $T_6=0.01$). However, at relativistic high temperature (e.g. $T_6=10$), the observations $L_{\mathrm{\text{rad}}}$ can be four and two orders of magnitude lower than those of models (I) and (II), respectively. We also compared the results of models (I) and (II) by scaling factor $k_3$. One can see that the maximum of the luminosities for model (I) are 185.2705 and 512.7054 times larger than those of model (II) for old WD $1247+551^a$ at $T_6=0.01$, 10, respectively. On the other hand, the minimum of the luminosities for model (I) are 7.3563 and 34.8064 times larger than those of model (II) for old WD 1444-175 at $T_6=0.01$, 10, respectively. By considering the effect on the mass radius relationship by the number of the MMs captured in WDs and catalytic nuclear decay, our results show that the study of model (II) may be an improving estimation, and the monopole-catalyzed nucleon decay process could be preventing white dwarfs from cooling down into a stellar graveyard by keeping them hot.

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

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.

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.

An analytical and nonperturbative approach to SU(2) and SU(3) Yang–Mills thermodynamics is developed and applied. Each theory comes in three phases: A deconfining, a preconfining, and a confining one. We show how macroscopic and inert scalar fields emerge in each phase and how they determine the ground-state physics and the properties of the excitations. While the excitations in the deconfining and preconfining phases are massless or massive gauge modes the excitations in the confining phase are massless or massive spin-1/2 fermions. The nature of the two phase transitions is investigated for each theory. We compute the temperature evolution of thermodynamical quantities in the deconfining and preconfining phase and estimate the density of states in the confining phase. Some implications for particle physics and cosmology are discussed.

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.

It has been known for 30 years that 't Hooft–Polyakov monopoles of charge Q greater than one cannot be spherically symmetric. Five years ago, Bolognesi conjectured that, at some point in their moduli space, BPS monopoles can become approximately spherically symmetric in the high Q limit. In this paper, we determine the sense in which this conjecture is correct. We consider an SU(2) gauge theory with an adjoint scalar field, and numerically find configurations with Q units of magnetic charge and a mass which is roughly linear in Q, for example, in the case Q = 81 we present a configuration whose energy exceeds the BPS bound by about 54%. These approximate solutions are constructed by gluing together Q cones, each of which contains a single unit of magnetic charge. In each cone, the energy is largest in the core, and so a constant energy density surface contains Q peaks and thus resembles a sea urchin.