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Register a new userThe Heavy Dirac Monopole
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P. Pitanga
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We present a model for the Dirac magnetic monopole, suitable for the strong coupling regime. The magnetic monopole is static, has charge g and mass M, occupying a volume of radius R ~ O (g^2/M). It is shown that inside each n-monopole there exist infinite multipoles. It is given an analytical proof of the existence of monopole-antimonopole bound state. Theses bound-states might give additional strong light to light scattering in the proton-antiproton collision process at FermiLab TEVATRON.
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Writing the metric of an asymptotically flat spacetime in Bondi coordinates provides an elegant way of formulating the Einstein equation as a characteristic value problem. In this setting, we find that a specific class of asymptotically flat spacetimes, including stationary solutions, contains a Maxwell gauge field as free data. Choosing this gauge field to correspond to the Dirac monopole, we derive the Taub-NUT solution in Bondi coordinates.
Berrys phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model. This topology change of Berrys phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berrys phase is determined by a simple geometrical consideration of the magnetic flux coming from the displaced Dirac monopole.
In the previous papers, we studied the t Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that the configuration space can be classified into the topological sectors. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and consider the index theorem in these cases.
We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background. Using these modes, we then compute the fermionic condensate, $langle 0| overline{Psi} Psi | 0rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field. We have used the Abel-Plana summation formula in order to extract the pure global monopole contribution to these quantities and have investigated their variations numerically with respect to suitable parameters. Also in particular, by taking the massless limit for the components of the energy-momentum tensor we show that the global monopole cannot induce any contribution to the trace anomaly.
We show theoretically that a monopole defect, analogous to the Dirac magnetic monopole, may exist as the ground state of a dilute spin-1 Bose-Einstein condensate. The ground-state monopole is not attached to a single semi-infinite Dirac string, but forms a point where the circulation of a single vortex line is reversed. Furthermore, the three-dimensional dynamics of this monopole defect are studied after the magnetic field pinning the monopole is removed and the emergence of antimonopoles is observed. Our scheme is experimentally realizable with the present-day state of the art.
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