Monopole System Research Articles

A study of the analogue compensating monopole system for active attenuation of noise in a duct

This paper describes theoretically the feedback effect of the secondary source on the primary source in a monopole system for active attenuation of noise in a duct, and gives a more accurate mathematical model. Based on the model mentioned above, a new monopole system called the Analogue Compensating Monopole System, or ACM-System for short, is established. An analogue method for compensating the non-ideal phase response of the system is suggested and discussed, and measures for improving the non-ideal amplitude response are proposed. In order to improve the working stability of the system, a directional sound detector is introduced, and the absolute stability condition of the ACM-System is given. Test results show that the method for compensating for the phase errors and improving the amplitude characteristics of the system is effective. Experimental data from the ACM-System in conditions of flowing and quiet air in the duct are processed. Test results show that the ACM-System has a noise reduction ability superior to that of other monopole systems, whether in narrow or wider frequency bandwidths.

Noncanonical groups of transformations, anomalies, and cohomology

Two cohomology classes associated to groups of transformations (symplectic or not) of Hamiltonian and Lagrangian systems are studied. A geometrical interpretation of the family of cocycles arising from a class of nonsymplectic actions is given in terms of the Poisson structure of the phase space of the system. These ideas are used to study nongauge (i.e., anomalous) groups of transformations of (locally or globally defined) Lagrangian systems. In particular, well-known results about the magnetic monopole system are described in this context and some hints relating Yang–Mills anomalies with nonsymplectic groups of transformations are given.

Second-order systems with Runge-Lenz-type vectors

A class of second-order equation fields which contains the equations of motion of the Kepler and charge monopole problems is considered. In particular, the problems of the existence of a second integral of motion quadratic in momenta besides the energy is investigated and completely solved. A subclass of systems is exhibited which have a Runge-Lenz-type vector, but it is shown that the monopole system itself has no second (time-independent) quadratic integral of motion.

Fermions and non-Abelian vortex

Discusses some aspects of the fermion-non-Abelian vortex system. It is shown that this system has properties analogous to those of the fermion-non-Abelian magnetic monopole system. However, in contrast to the fermion-monopole case, this system does not give rise to the fermion condensate ( psi psi )v=0.

The O(3,1) symmetry problem of the charge–monopole interaction

The question of whether there exists a smooth, time-independent conserved vector observable in the classical mechanics of the charge–monopole interaction that spans an O(3,1) Lie algebra together with the angular momentum or not is examined. It turns out that any candidate for such dynamical symmetry algebra has hard singularities at that part of the phase space that corresponds to charge–monopole collisions. In the course of the investigation we use the transformation of Boulware et al. [D. G. Boulware, L. S. Brown, R. N. Cahn, S. D. Ellis, and C. Lee, Phys. Rev. D 14, 2708 (1976)] relating the charge–monopole system to a point mass moving in an inverse square potential. This transformation is shown to be a complete isomorphism between the scattering parts of the related Hamiltonian systems; its global behavior is described in terms of an U(1) principal fiber bundle of nontrivial topology. Several remarks on the symmetries of various monopole problems are made, e.g., the most general O(4) symmetry algebra is given for a special form of the charge–dyon interaction.

Bound states, resonances, and symmetries of a neutral Dirac particle with anomalous magnetic moment, coupled to a fixed monopole

For the system consisting of a neutral Dirac particle with anomalous magnetic moment, interacting with a fixed magnetic monopole, zero-energy bound states are constructed for each possible value of the total angular momentum. Results of Kazama and Yang for the charge–monopole system are used to deduce the existence of other bound states for this system, when the mass of the bound particle is nonzero. In the zero-mass case, there are no other bound states, but there are resonant states, and these are determined exactly. A noncompact, so(3,2) symmetry algebra of the zero-energy bound states is given for the finite-mass case and for the zero-mass case. In each case the infinite number of such states is associated with an irreducible Majorana representation of the algebra.

New selection rules for the SU(5) monopole catalyzed proton decay reactions

We show that a complete treatment of all the gauge forces experienced by massless s-wave fermions in the SU(5) monopole system leads to new selection rules, previously overlooked in the bosonization treatment in which only abelian gauge fields were considered. The most important consequence of these selection rules is that the catalysis reaction requires an anomaly driven process, the pure boundary condition driven process being highly suppressed. At first sight, this means that one cannot ignore the heavy generations, and consequently the reaction is suppressed. We give arguments why this is in fact not the case.

The s-wave SU(5) monopole-fermion system reduces to a coupled set of exactly solvable QFTs

By establishing that the SU(2) colour sector of fermions in the SU(5) 't Hooft-Polyakov monopole system has an underlying SU(2) Kac-Moody algebra with central charge unity, we show for massless fermions that the whole system can be reduced to a coupled set of exactly integrable two-dimensional QFT's in radial space. Consequently all the non-perturbative effects in the Green functions governing baryon number non-conservation can be explicitly computed up to the effect of the ordinary QCD confining vacuum, which is relevant only at long distances from the monopole's core.

Is electric charge conserved in monopole-fermion scattering?

By integrating exactly the effective Bose field theory which describes the s-wave fermion-magnetic monopole system, the authors show that the condensate around a gauge theory monopole is electrically neutral. So the fermion-monopole scattering is of pure helicity flip due to the chiral condensate.

Power requirements for active noise control in ducts

Active attenuation of noise in a duct generally requires either one or two rings of cancelling loudspeakers located around the duct perimeter. Consideration is given to the acoustic loading on the loudspeakers and it is shown that the use of a horn is likely to create more problems that it solves. Direct radiator operation, with the drive units attached directly to the duct walls, is preferable. The single ring (monopole) system reflects the noise giving rise to upstream standing waves, meaning that the loudspeakers and amplifiers must be able to handle correspondingly larger signals. The double ring (dipole) system absorbs the noise and is more efficient than the monopole system. The dipole system can be made still more efficient over a narrow band of frequencies by tuning both the loudspeakers and the spacing between them.

Active attenuation of noise—The monopole system

Proposals have been made to attenuate noise propagating down a duct by adding an antiphase copy of the primary noise. In a number of configurations, two or three sources had been used to produce the secondary noise, but a successful system with one source had not been realized. The conventional monopole system is analyzed and the reason why this type of monopole secondary source is not a practical solution is investigated. A modified system with a new solution of the problem is developed.

Supersymmetric point particles and monopoles with no strings

In previous work, an action principle for the charge monopole system was developed and it was canonically quantized. The action was single valued and free of string singularities. In this work, we supersymmetrize the preceding action and canonically quantize this new action. It describes a charged spin-half particle of gyromagnetic ratio 2 in a magnetic monopole field. It is shown that if a system admits only local lagrangians for a configuration space Q, then under certain conditions, it admits a global lagrangian when Q is enlarged to a suitable U(1) bundle over Q. (The charge monopole system is an example of such a system.) Conditions under which a symplectic form is derivable from a lagrangian are also found.

Integral equations for extended solutions in field theory: Monopoles and dyons

In this paper we give a simple method to obtain extended solutions of nonlinear classical field theories. The technique applies to problems where the boundary values at either end of the domain are specified, and consists of converting the set of field equations to a system of coupled nonlinear integral equations that can be solved numerically by simple iteration. As an illustration, the 't Hooft monopole and the Julia-Zee dually charged monopole system are studied in detail. The physical structure of these extended solutions and the possible effects of quantum fluctuations are briefly discussed.