Exact magnetic monopole solutions in Yang-Mills and unified gauge theories

We study the magnetic monopoles in non-Abelian gauge theories. The exact static, spherically symmetric solutions of the magnetic monopoles in both Yang-Mills and unified gauge theories are obtained. The energyE of the static system is calculable and it is either zero or infinite. The existence of the magnetic monopole solution is a consequence of symmetry rather than dynamics. We propose a new definition of the electromagnetic field tensor, which relates the static solution of gauge fields and the magnetic monopole solution. Experimental implications are discussed.     

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.     

Monopole and topological electron dynamics in adiabatic spintronic and graphene systems

A unified theoretical treatment is presented to describe the physics of electron dynamics in semiconductor and graphene systems. Electron spin's fast alignment with the Zeeman magnetic field (physical or effective) is treated as a form of adiabatic spin evolution which necessarily generates a monopole in magnetic space. One could transform this monopole into the physical and intuitive topological magnetic fields in the useful momentum (K) or real spaces (R). The physics of electron dynamics related to spin Hall, torque, oscillations and other technologically useful spinor effects can be inferred from the topological magnetic fields in spintronic, graphene and other SU(2) systems.     

Monopoles and topological field theory

We present a topological quantum field theory for magnetic monopoles in an SU(N) Yang-Mills-Higgs model. This field theory is obtained by gauge fixing the topological action defining the monopole charge. This work extends to the three-dimensional case the quantization of invariant polynomials in four dimensions. We choose the Bogomolny self-duality equations as gauge conditions for the magnetic monopole topological field theory. In this way the geometrical equation discussed e.g. in Atiyah and Hitchin's work are recovered as ghost equations of motion. We give the cocycles of the corresponding topological symmetry. In the N→∞ limit interesting phenomena occur. The functional integration is forced to cover only the moduli space and the role of the ghosts stemming from the gauge fixing process is to provide a smooth semiclassical approximation.     

Star-product in the presence of a monopole

We present a deformed ?-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in ?) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.     

Search for neutrino-produced magnetic monopoles in a bubble chamber exposure

J. Schwinger has suggested that magnetically charged particles could be produced via a magnetically charged intermediate boson process similar to the mechanism sometimes envisioned for double muon production by neutrinos. A search for magnetic monopole production by neutrinos has been made by reexamining the CERN heavy liquid bubble chamber pictures obtained during the neutrino exposures of 1963 and 1967. Five different searches were made for events which contained a free monopole with and without target nucleus excitation, and for bound monopoles which deexcited by photon emission. No events were found. Neutrino monopole production cross-section limits are given.     

Kinematics of Yang-Mills solitons

In SU(2) Yang-Mills theory, theN-monopole configuration space is a bundle with fibers isomorphic to U(1)×...×U(1), and state vectors for which each monopole has chargen e/2 are homogeneous of degreen with respect to each U(1). Translations and rotations are defined for individual monopoles in theN-monopole space. The commutator of two translations is found to be a U(1) transformation that agrees for large monopole separation with the analogous phase change accompanying the translation of a charged point particle in an external magnetic field. The theory developed here is applied in a companion paper to prove a spin-statistics theorem for monopoles in SU(2) Yang-Mills theory.     

Cherenkov magnon excitations by a sub-relativistic magnetic monopole

A magnetic monopole moving faster than the magnon phase velocity in a given magnetic medium will create a magnon Cherenkov radiation in this medium. Typical velocities of interest are in the ～10^?4c range. In this range most non-induction detection mechanisms are inefficient.     

Magnetic backgrounds from generalised complex manifolds

The magnetic backgrounds that physically give rise to spacetime noncommutativity are generally treated using noncommutative geometry. In this paper we prove that also the theory of generalised complex manifolds contains the necessary elements to generate B-fields geometrically. As an example, the Poisson brackets of the Landau model (electric charges on a plane subject to an external, particularly applied magnetic field) are rederived using the techniques of generalised complex manifolds.     

Gauged Laplacians on Quantum Hopf Bundles

We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe ‘excitations moving on the quantum sphere’ in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.     

Scattering of fermions on the SU(5) colorless magnetic monopole

We discuss the scattering of fermions (d?, u-quarks and e^c) on the SU(5) colorless magnetic monopole. The radial functions of scattering wave are totally separated from the angular parts in the Dirac equations which then reduce to a set of coupled ordinary differential equations. We solve these equations numerically for the d?e^c group with j = 1, and get the result that only the incoming wave of d with j = 1 and j′ = 0 can be scattered into e^c. The cross section is obtained which is intimately connected with the catalysis effect of the monopole for baryon decay.     

Dynamical symmetry of the magnetic monopole

It is demonstrated that the interaction of a charged particle with a magnetic monopole possesses a large invariance; time can be arbitrarily re-parametrized. When the interaction occurs within conventional, non-relativistic dynamics, the entire theory admits an O(2, 1) conformal group of symmetry transformations, which seems to have escaped notice. Combining this invariance group with the O(3) group of spatial rotations shows that an O(2, 1) × O(3) group of invariances is present, in analogy with the Kepler/Coulomb system. Furthermore, at fixed angular momentum, the dynamics are characterized by a single, irreducible, unitary representation of the conformal O(2, 1) symmetry group, whose Casimir eigenvalue is determined by the monopole strength. Some similar properties of the isotropic harmonic oscillator are also mentioned.     

Spectrum of Schrödinger field in a noncommutative magnetic monopole

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged Schrödinger field coupled to a noncommutative U(1) gauge field is identified. It is shown that the Hamiltonian is essentially the angular momentum squared of the particle, but with a nontrivial scaling factor appearing, in agreement with the first-quantized canonical treatment of the problem. Monopole quantization is recovered and identified as the quantization of a commutative Seiberg–Witten mapped monopole field.     

由正负磁单极对相互作用诱导的孤立狄拉克弦

基于三维旋量Gross-Pitaevskii(GP)方程研究在含时周期性外磁场作用下玻色-爱因斯坦凝聚体的动力学行为.结果显示,在含时周期外磁场的作用下,铁磁态自旋为1的玻色-爱因斯坦凝聚体将发生拓扑形变.当磁场的两个零点进入凝聚体后,自旋向上态的密度布居图在z轴上分别形成向上和向下的凸起.随着磁场的两个零点在凝聚体内逐渐重合,向上和向下的凸起被拉长,最终自旋向上态在z轴上呈线状分布,这与理论分析预测得到的孤立狄拉克弦相对应.最后,通过计算凝聚体的超流涡度给出磁单极的表征图.结果显示,凝聚体在磁场的两个零点处形成正、负磁单极对,分别对应着自旋向上态在z轴上向上和向下的凸起.随着磁场的两个零点重合,正、负磁单极对中的两条狄拉克弦逐渐靠近,之后大约经5 ms,它们完全相连,最终形成孤立的狄拉克弦.     

Classical solutions of Yang-Mills and CP n−1 models with scalar fields

We present a study of classical solutions of the SU(2) Yang-Mills (YM) theory with a massless Higgs doublet, and of the CP ^n?1 model coupled to a scalar field. In both cases the scalar field tends to suppress instantons but not merons (this is a purely classical effect). In the YM theory a static Wu-Yang-like monopole solution with variable magnetic charge is found and its connection with the meron solution of this theory is discussed.     

Bound states of scalar and spinor particles with arbitrary isospin in the regular Dyon field

The problem of bound states of the spinor and scalar particles with arbitrary isospin on the back-ground of regular magnetic monopole and dyon solution of theSU(2) gauge system is considered using Newman-Penrose formalism. The explicit general formulas for the energy eigenvalues are obtained which are in agreement with many particular cases described earlier.     

The isovector monopole state and the escape width of double analog resonances

An irreducible vector operator is used to generate isovector monopole states with welldefined values of T and T_z in N > Z nuclei. Reduced transition strengths are calculated in two different ways and the results seem compatible. The Wigner-Eckart theorem is used to derive expressions for the mixing of the monopole states with the ground state and its analog states. Expressions for the escape widths of the monopole states are also derived. An application is made to double analog resonances, and it is found, contrary to expectations, that the mixing with the T?1 monopole state is unable to account for the observed elastic partial width of these resonances in medium and heavy nuclei. The reason for this is the small escape width of the monopole state.     

Group structure of an isospin-invariant fermion dynamical symmetry model

The monopole and quadrupole pairing model (fermion dynamical symmetry model) is generalised by the addition of isospin to allow applications to nuclei with valence protons and neutrons in the same shells, and the corresponding group chains are determined. Two distinct rotational limits are found.     

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.