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.     

Commutative asymptotic limit of a quasi-SU(2) formulation of general relativity

The notion of local quasi-gauge bundle structure is introduced. We show that general relativity can be recast in a local quasi-SU(2)-bundle framework. In the limit of weak asymptotic gravitational field, this geometrical setup gives rise to spin-2 tensor fields sourcing global charges. If such charges are available, it is shown that the asymptotic geometrical framework is that of aU(1) gauge bundle overS ₂, the commutative geometry of the (Dirac) magnetic monopole.     

A method to compare quark and gluon jets in $$e^ + e^ - \to q\bar qg$$ hadronisation

The conserved charges of non-abelian gauge theories are systematically investigated in the framework of the manifestly-covariant canonical formalism. An internal-symmetry superalgebra consisting of 4n+5 generators is found in the Landaugauge case of the Yang-Mills theory, wheren denotes the dimension of the gauge group. Likewise, a superalgebra consisting of 4×6+5 generators is found in the internal-Lorentz (local-Lorentz) part of the vierbein formalism of quantum gravity. It is pointed out that there is a complete parallelism between both superalgebras.     

Anomalous angular momenta in a quantised theory of monopoles

In this paper a gauge theory with a classical solution corresponding to a magnetic monopole is quantised. By careful handling of the zero frequency modes it is shown that the monopole is capable of absorbing both momentum and charge. The angular momentum operator is considered and it is shown that if the original theory contains an isodoublet scalar field, the quantum excitations may be half odd integer eigenvalue eigenstates of this operator.     

Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity

It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.     

Generalised magnetic monopole for the yang-mills field

By analogy to the magnetic monopole first proposed by Dirac (1931), a generalised magnetic monopole, being a source of the Yang-Mills field, is constructed. The gauge invariance and the rotational symmetry lead in a natural way to the quantisation not only of the electric charge but also of the hypercharge numberY. It is shown that the generalised magnetic charges are not arbitrary, and some restrictions on their values are deduced.     

Monopole effects,core excitations,and β decay in the A = 130 hole nuclei near ~(132)Sn

The proton and neutron cross-shell excitations across the Z = 50 shell are investigated in the southwest quadrant of ~(132) Sn by large-scale shell-model calculations with extended pairing and multipole-multipole force. The model space allows proton(neutron) core excitations, and both the low-and high-energy states for ~(130) In are well described, as found by comparison with the experimental data. The monopole effects between the proton orbit and neutron orbit are studied as the new monopole correction that perfectly reproduces the first 1~+ level in ~(130) In. The energy interval of proton(neutron) core excitations in ~(130) In lies in the range of 4.5-6.5(2.0-4.1) MeV, and the high energy yrast states are predicted as neutron core excitations. The decays are calculated among the A=130 nuclei of ~(130) In, ~(130) Sn and ~(130) Cd.     

Charge definition in non-abelian gauge theories

Conserved gauge-invariant electric and magnetic charges are defined for non-abelian gauge theories in terms of the asymptotic symmetries of the field configurations. They are expressed as flux integrals. Illustrations include the magnetic charge of the 't Hooft-Polyakov monopole and the electric and magnetic charges of the Julia-Zee dyon.     

The nut solution as a gravitational dyon

Linearized theory suggests that the NUT solution of Einstein's equations corresponds to a source with both mass and dual mass i.e. to a gravitational dyon. This is born out by the striking identity between the Killing operators of the NUT solution and the ‘total angular momentum’ operators of the monopole. On this basis, Misner's periodic time condition is shown to be the analogue of the Dirac quantization, and results from the requirement that the generators integrate to a global Lie group. It is also shown that there are no bound states for a Klein-Gordon field in NUT space provided the field vanishes in the conventional way at the horizon. For this purpose a generalized ‘tortoise coordinate’ is introduced.     

Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

Magnetic monopole solutions for an arbitrary compact simple gauge group are considered in the Prasad-Sommerfield limit. For each group and choice of symmetry breaking there is a set of fundamental monopoles with minimal topological charges and possessing no internal degrees of freedom; the number of these is less than or equal to the rank of the gauge group. It is shown that if the unbroken gauge group is abelian, all solutions with higher topological charges belong to p-parameter families, where p is the number of position and group orientation parameters needed to describe a set of non-interacting fundamental monopoles with the given topological charge. It is argued that these solutions, some examples of which are given, should therefore be interpreted as multimonopole configurations. An extension of these results to the case of a non-albelian unbroken gauge symmetry is conjecture and shown to be valid for a number of examples.     

Momentum dependence of polarization charges in electron excitation of nuclei in the oxygen region

We have considered the polarization effects for monopole and quadrupole electron excitations of nuclei in the oxygen region. A phenomenological method has been used in order to extrapolate empirical values for the polarization charges, from the real photon limit, to higher momentum transfers. We find in most cases polarization charges that are nearly constant, for momentum transfers up to 2 or 3 fm^?1. Hence we have provided a justification in the oxygen region for the assumption most frequently made when experiment and theory are compared.     

Wave equation for a magnetic monopole

We show that there is room, in the Dirac equation, for a massless monopole. The basic idea is that the Dirac equation admits a second electromagnetic minimal coupling associated to the chiral gauge , which is only valid for a massless particle, but satisfies all the symmetry laws of a monopole. In the problem of the diffusion on a central electric field, we find the Poincaré integral and the Dirac relationeg/=n/2. The latter is deduced as a consequence of the fact (which is shown in this paper) thateg/c is the projection of the total angular momentum on the symmetry axis of the system formed by the monopole and the electric charge. Another important property is that a monopole and an antimonopole have opposite helicities (as for the neutrino), but do not have opposite charges: this precludes a vacuum magnetic polarization which would be analogous to the electric one, but allows us to imagine an aether made up of monopole-antimonopole pairs. The theory is then generalized on the basis of a nonlinear equation which is the most general invariant equation under the chiral gauge law. This equation admits solutions corresponding to massive monopoles, among which there are bradyons (i.e., ordinary massive particles) and tachyons. This equation is shown to be closely related to previous works initiated by Hermann Weyl, on Dirac's theory in the framework of general relativity. In conclusion, it is suggested that massless monopoles are perhaps excited states of the neutrino and that they may be produced in some weak interactions. Consequences on the solar activity are considered.     

Fermions and spherically symmetric monopoles

The interaction of fermions with monopoles is analyzed for general spherically symmetric monopoles of arbitrary strength and massless fermions in arbitrary representations of the gauge group. The results are based on a solution to the Dirac equation in the field of the monopole, valid in the point limit and in all partial waves. The partial waves in which non-conservation of global charges may occur are identified. A two-dimensional lagrangian is derived, which includes the Coulomb interactions generated by the complete abelian subgroup of the unbroken gauge group. The fermions are represented by a set of doublets with a boundary condition that reflects the structure of the core. We derive a simple formula for the conservation laws of this model which determine all scattering processes completely. The results have a consistent interpretation in terms of anomalies and field configurations with non-trivial winding number. We give an explicit construction of the zero modes for all helicity-violating multi-fermion condensates. The formalism is applied to several higher strength monopoles in SO(10) based models.     

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.     

Isoscalar Monopole Excitations and Cluster Structures in Light Nuclei

Isoscalar monopole excitation to cluster states in light nuclei is in general strong as to be comparable with the single particle strength and shares about 20 % of the sum rule value. The isoscalar monopole strength function in ¹⁶O is discussed up to ${E_x \lesssim 40 \, {\rm MeV}.}$ We found that (1) two different types of monopole excitations exist in ¹⁶O; one is the monopole excitation to cluster states which is dominant in the lower energy part, and the other is the monopole excitation of the mean-field type such as one-particle one-hole (1p1h) which is attributed mainly to the higher energy part, and (2) this character of the monopole excitations originates from the fact that the ground state of ¹⁶O with the dominant doubly closed shell structure has a duality of the mean-field-type as well as alpha-clustering character.     

Topological field patterns in the Yang-Mills theory

We present a formalism where the topological configurations of pure Yang-Mills theory are characterised using gauge fields alone. Here, we obtain an expression for the charges of these topologicalSO(3) gauge field configurations in terms of the Abelian vector potentials. In this formalism we analyse the ’t Hooft-Polyakov monopole solution.     

Spin ice: magnetic excitations without monopole signatures using muon spin rotation

Theory predicts the low temperature magnetic excitations in spin ices consist of deconfined magnetic charges, or monopoles. A recent transverse-field (TF) muon spin rotation (μSR) experiment [S.?T. Bramwell et al., Nature (London) 461, 956 (2009)] reports results claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation-the so-called second Wien effect. We demonstrate via a new series of μSR experiments in Dy(2)Ti(2)O(7) that such an effect is not observable in a TF μSR experiment. Rather, as found in many highly frustrated magnetic materials, we observe spin fluctuations which become temperature independent at low temperatures, behavior which dominates over any possible signature of thermally nucleated monopole excitations.     

Appearance of gauge potentials in atomic collision physics

The dynamical equations obtained from the method of perturbed stationary states (PSS) are shown to be formally equivalent to the dynamical equations of a particle with N internal degrees of freedom minimally coupled to U (N) static gauge potentials. Several examples are given that illustrate the appearance of non-abelian and magnetic monopole gauge potentials in simple systems. Advantages of expressing the PSS equations as a gauge theory are discussed.