The one and a half monopoles solution of the SU(2) Yang–Mills–Higgs field theory

Recently we have reported on the existence of finite energy SU(2) Yang–Mills–Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft–Polyakov monopole. The magnetic charge of the one-half monopole is of opposite sign to the magnetic charge of the ’t Hooft–Polyakov monopole. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z$z$-axis that carries the other half of the magnetic monopole charge. The solution possesses gauge potentials that are singular along the z$z$-axis, elsewhere they are regular. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ$\lambda$. However the dipole separation and the magnetic dipole moment decrease with λ$\lambda$. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.     

A Clifford Algebra Approach to the Classical Problem of a Charge in a Magnetic Monopole Field

The motion of an electric charge in the field of a magnetic monopole is described by means of a Lagrangian model written in terms of the Clifford algebra of the physical space. The equations of motion are written in terms of a radial equation (involving r=|r|, where r(t) is the charge trajectory) and a rotor equation (written in terms of an unitary operator spinor R). The solution corresponding to the charge trajectory in the field of a magnetic monopole is given in parametric form. The model can be generalized in order to describe the motion of a charge in the field of a magnetic monopole and other additional central forces, and as an example, we discuss the classical ones involving linear and inverse square interactions.     

A Gauge Theoretical View of the Charge Concept in Einstein Gravity

We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension /l ², the mass parameter of a particle dimension /l, and the Schwarzschild mass parameter dimension l (where l means length). These dimensions confirm the meaning of mass as elementary and as monopole charge of the translation group, respectively. In detail, we find that the Schwarzschild mass parameter is a quasi–electric monopole charge of the time translation whereas the NUT parameter is a quasi–magnetic monopole charge of the time translation as well as a topological charge. The Kerr parameter and the electric and magnetic charges are interpreted similarly. We conclude that each elementary charge of a Casimir operator of the gauge group is the source of a (quasi-electric) monopole charge of the respective Killing vector.     

Colored monopole and strong CP

A systematic application of the collective coordinate method to quantization of spontaneously broken gauge theories with fermions, such as GUTs, in the monopole sector is presented. Usual and unusual charge properties of the ground state GUT monopole induced by CP violation, and in particular by the fact that θ_QCD ≠ θ_EM, are studied. In the presence of axions, semiclassically the ground state of GUT monopole is an actual realization of a spherical color-capacitor with the capacitance controlled by the magnitude of the Peccei-Quinn symmetry breaking scale. The “vacuum” around it is characterized by strongly enhanced (strong) CP violation and extends considerably far outside the monopole core. The effect of light fermions is studied in some detail. The possibility that even in the presence of axions (i.e. θ_QCD=0) there might be a non-vanishing and, in general, order-one color electric charge on the monopole ground state is pointed out.     

Magnetic Monopoles in U(1)4 Lattice Gauge Theory with Wilson Action

We construct the Euclidean Green functions for the soliton (magnetic monopole) field in the U(1)₄ Lattice Gauge Theory with Wilson action. We show that in the strong coupling regime there is monopole condensation while in the QED phase the physical Hilbert space splits into orthogonal soliton sectors labeled by integer magnetic charge. Received: 2 July 1997 / Accepted: 20 July 1998     

<Emphasis Type="Italic">N</Emphasis>=2 de Sitter Super-symmetry Algebra

It was shown that N=1 super-symmetry algebra can be constructed in de Sitter space (Pahlavan et al. in Phys Lett. B 627:217–223, 2005), through calculation of charge conjugation in the ambient space notation (Moradi et al. in Phys. Lett. B 613:74, 2005; Phys. Lett. B 658:284, 2008). Calculation of N=2 super-symmetry algebra constitutes the main frame of this paper. N=2 super-symmetry algebra was presented in Pilch et al. (Commun. Math. Phys. 98:105, 1985). In this paper, we obtain an alternative N=2 super-symmetry algebra.     

Existence of Static BPS Monopoles and Dyons in Arbitrary (4p – 1)-Dimensional Spaces

We prove the existence and uniqueness of a static and radially symmetric BPS monopole of unit topological charge in an arbitrary (4p – 1)-dimensional space descended from the generalized Yang–Mills theory in 4p dimensions and formulated and presented in a recent study of Radu and Tchrakian. This monopole solution also gives rise to an electrically and magnetically charged soliton, called dyon, in the same spacetime setting through the well-known Julia–Zee correspondence. Our method is based on a dynamical shooting approach depending on two shooting parameters which provides an effective framework for constructing the BPS monopole and dyon solutions in general dimensions.     

Electromagnetic decay of the 02+ state in the doubly closed shell nucleus 64146Gd82

The existence of the 0₂⁺ state in ¹⁴⁶Gd at 2165.0 (4) keV is established through observation of the E0(0₂⁺ → 0₁⁺ transition. The measured half-time 375 (40) ps of this state corresponds to a monopole strength of ?² = 0.0122 (13) which is taken as evidence against a strong state dependence of the effective proton monopole charge.     

Schwarzschild black hole with global monopole charge

We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It turns out that existence, boundedness and stability of circular orbits scale up by (1−8πη ²)⁻¹, and the perihelion shift and the light bending by (1−8πη ²)^−3/2, while the Hawking temperature scales down by (1−8πη ²)² the Schwarzschild values. Hereη is the global charge.     

Integrality of the monopole number in SU(2) Yang-Mills-Higgs theory on ℝ3

We prove that in classical SU(2) Yang-Mills-Higgs theories on ³ with a Higgs field in the adjoint representation, an integer-valued monopole number (magnetic charge) is canonically defined for any finite-actionL _1,loc ² configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components.Research supported in part by NSF Grants 8120790 and PHY-03669     

Exact monopole solutions in gauge theories for an arbitrary semisimple compact group

We construct an exact n-parametric monopole and dyon solutions for an arbitrary compact gauge group G of rank n by using the symmetry between cylindrically symmetric instanton equations in Euclidean space R ₄ and monopole equations in Minkowski space R _3,1 (with Higgs scalar field in adjoint representation). The solutions are spherically symmetric with respect to the total momentum operator represents the minimal embedding of SU(2) in G. Explicit expressions for the monopole magnetic charge and mass matrices are obtained. The remarkable aspect of our results is the existence of discrete series of the monopole solutions, which are labelled by n quantum numbers and degenerated in the latter ones at a fixed monopole mass matrix.     

Ann monopole solution with 4n — 1 degrees of freedom

An exact static monopole solution, possessingn units of magnetic charge and (4n-1) degrees of freedom, is constructed, generalising the recent work of Ward on two monopole solutions. The equations solved are those of anSU(2) gauge theory with adjoint representation Higgs field in the (BPS) limit of vanishing Higgs potential. The number of degrees of freedom is maximal for self-dual solutions. The construction is described in a deductive way, within the framework of the Atiyah-Ward formalism for self-dual gauge fields.     

Monopole charge quantization or why electromagnetism is a U(1)-gauge theory

We obtain Dirac’s classic monopole charge quantization from the point of view of geometric quantization and demonstrate how this leads to the conclusion that the electromagnetic field is a U(1)-gauge field.     

Platonic Hyperbolic Monopoles

We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in ${\mathbb{R}^4}$ that are invariant under a circle action, and in most cases the monopole charge is equal to the instanton charge. A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance. Unlike for Euclidean monopoles, the formulae for the squared Higgs field magnitude in the examples we construct are rational functions of the coordinates. Using these formulae, we compute and illustrate the energy density of the monopoles. We also prove, for particular monopoles, that the number of zeros of the Higgs field is greater than the monopole charge, confirming numerical results established earlier for Euclidean monopoles. We also present some one-parameter families of monopoles analogous to known scattering events for Euclidean monopoles within the geodesic approximation.     

Anomalous baryon number non-conservation in the presence of SU(5) monopoles

It is shown that the effects related to the Adler-Bell-Jackiw anomaly give rise to strong baryon number non-conservation in the presence of magnetic monopoles in the SU(5) grand unified theory. The main assumption made is that, as long as distances of order 1 GeV^?1 from the monopole center are considered, the masses of light fermions u, d, s, e, μ can be neglected, while heavy fermions decouple. Two types of the SU(5) monopoles are studied, namely: (i) the fundamental monopole with a non-vanishing chromomagnetic charge, (ii) the minimal purely electromagnetic monopole. In both cases the processes like

$\text{p}\text{+}\text{monopole}\text{→}\text{e}{}^{\mathrm{+}}\text{+}\text{momopole}\text{+}\text{everything}$

are allowed. It is argued that the cross sections of these processes are of order 1 GeV^?2β^?2, at least for sufficiently low monopole-proton relative velocities β.     

Monopoles,baryon decay and charge conservation

The mechanism of baryon decay via monopoles is analyzed. For this purpose we quantize isodoublet fermion fields in the presence of a 't Hooft-Polyakov monopole. When the electromagnetic interactions are switched off, we find a condensation of a fermion pair \(\bar \psi _ - ^{(i)} \gamma ^0 \gamma ^5 \psi _ + ^{(i)} \) as well as that of \(\bar \psi _ - ^{(i)} \gamma ^0 \gamma ^5 \psi _ + ^{(i)} \bar \psi _ + ^{(j)} \gamma ^0 \gamma ^5 \psi _ - ^{(j)} \) . Here, the indices ± stand for the electric charge and (i,j) for the flavour. Hence, the charge symmetry is spontaneously broken. However, when the Coulomb interactions are switched on, it is proved that all fermion condensates carrying non-zero electric charges are removed; the condensates carrying zero electric charge, which induce baryon decay in the standardSU (5) model, are not removed by switching on the Coulomb interactions. In these analyses, the key element is the charge mixing boundary condition imposed on the fermion wave-function at the monopole center; the chiral anomaly does not play any role.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) global monopole revisited

In this paper the f(R) global monopole is reexamined. We provide an exact solution for the modified field equations in the presence of a global monopole for regions outside its core, generalizing previous results. Additionally, we discuss some particular cases obtained from this solution. We consider a setup consisting of a possible Schwarzschild black hole that absorbs the topological defect, giving rise to a static black hole endowed with a monopole’s charge. Besides, we demonstrate how the asymptotic behavior of the Higgs field far from the monopole’s core is shaped by a class of spacetime metrics which includes the ones analyzed here. In order to assess the gravitational properties of this system, we analyze the geodesic motion of both massive and massless test particles moving in the vicinity of such configuration. For the material particles we set the requirements they have to obey in order to experience stable orbits. On the other hand, for the photons we investigate how their trajectories are affected by the gravitational field of this black hole.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.