Algebraic construction of static axially symmetric self-dual gauge fields for an arbitrary group

It is suggested that the Higgs and the Yukawa couplings of the standard model possess two global U(1)-symmetries: independent chiral rotations of quarks and leptons. The model requires the existence of two axions, one of which (massive) does not interact with leptons, whereas the second one interacts both with leptons and quarks.     

Spherically symmetric equations in gauge theories for an arbitrary semisimple compact lie group

An explicit construction of spherically symmetric equations (not only static and/or self-dual) in gauge theories for the minimal embedding of SU(2) in an arbitrary semisimple compact Lie group G is given. The final equations are written in a form containing only gauge invariant quantities in R₂. The whole group structure is concentrated in the only matrix, which is directly related to the Cartan matrix of G. In particular, the developed technique allows to generalize the Witten duality equation [1] and to obtain the spectrum of pointlike solutions in G.     

On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.     

On axially symmetric solutions to the Higgs-Kibble-Yang-Mills field equations

The field equations for axially symmetric generalizations of the 't Hooft-Polyakov magnetic monopole are written out in a preferred coordinate system. It is argued that no soliton solutions exist when the product 2eg of the electric chargee with the magnetic chargeg is an even integer.Dedicated to Achille Papapetrou on the occasion of his retirement.     

A new construction technique for exact axially symmetric static electrovac solutions of the Einstein-Maxwell equations

Coordinates adapted to the full electrostatic symmetries of a charged axially symmetric static system are constructed and applied to the coupled Einstein-Maxwell equations. A new solution is presented and the framework for general solutions is developed. The Weyl solutions g₀₀(Φ) are readily extracted from the formalism.     

Criteria for the field boundaries of an axially symmetric ultrawideband radiator

Criteria for the near and far electromagnetic fields of ultrawideband radiation are considered based on a numerical simulation. To estimate the field boundaries for ultrawideband radiation, it is proposed to use the condition of the maximum (near field) and minimum (far field) differences between the time dependences of the electromagnetic field components. The approach proposed has been approved for an axially symmetric radiator excited by voltage pulses of varied waveform and duration. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–50, September, 2008.     

On a revisit to the Painlevé test for integrability and exact solutions for Yang’s self-dual equations forSU (2) gauge fields

Painlevé test (Jimboet al [1]) for integrability for the Yang’s self-dual equations forSU(2) gauge fields has been revisited. Jimboet al analysed the complex form of the equations with a rather restricted form of singularity manifold. They did not discuss exact solutions in that context. Here the analysis has been done starting from the real form of the same equations and keeping the singularity manifold completely general in nature. It has been found that the equations, in real form, pass the Painlevé test for integrability. The truncation procedure of the same analysis leads to non-trivial exact solutions obtained previously and auto-Backlund transformation between two pairs of those solutions     

On static,axially symmetric Einstein-Maxwell fields. Part I

The Weyl solution of the problem, obtained on the assumption thatg ₀₀ is a function of the electrostatic potential, is varied and the linearized field equations for the variation are discussed. The complete solution of the problem is determined for the special case of the Weyl solution that generalizes the Reissner-Nordstrom solution withm = ¦e¦.     

On the Atiyah-Drinfeld-Hitchin-Manin construction for self-dual gauge fields

The vector spacesA, B, C, in terms of which the general construction due to Atiyah, Drinfeld, Hitchin and Manin for self-dual gauge fields defined over some region of Euclidean space is phrased, are shown to be expressible in terms of the spaces spanned by the solutions of certain linear covariant differential equations depending on the gauge field. The corresponding linear maps betweenA andB, B andC are given with the properties required by ADHM and the results then necessary to verify the construction informally proved. The local problems associated with assuming the gauge field to obey the self-duality equations are separated from the global problems of assuring the required boundary conditions for a particular solution. With suitable global conditionsC is shown to be the dual ofA and a natural scalar product defined onB so as to reconstruct the gauge field in the standard form given by the construction. A discussion is given of the requirements entailed by the condition of a symmetry on the gauge field and the relation to the usual cohomological treatment is outlined in an appendix.On leave of absence from DAMTP, Silver Street, Cambridge, England     

On static,axially symmetric Einstein-Maxwell fields. Part II

Starting from the Reissner-Nordström solution withm =e we consider a variation representing a second particle situated outside the horizon. A formal dipole term in the potential of the second particle ensures equilibrium without additional stresses between the particles. The complete solution for the variation is determined and discussed in detail.     

也谈均匀磁场中旋转的中性轴对称导体上的电荷分布

严格证明了中性轴对称导体在均匀外磁场中旋转时,等势面为同轴圆柱面,并由电荷守恒定律证明该轴上的磁场精确等于外磁场Bo。同时还得出了该导体表面电荷密度的普遍公式。     

Singularities in solutions of the Einstein equations for a static spherically symmetric field

Russian Physics Journal - The nature of the singularities in the solutions of Einstein's equations for a static spherically symmetric field is investigated as a function of the choice of...     

均匀磁场中旋转的轴对称导体上的电荷分布析

分析了均匀磁场中旋转的轴对称导体上的电荷分布，指出这里不存在普遍的面电荷密度公式。     

New axially symmetric solutions of the Einstein-Maxwell equations

New exact solutions of the algebraic form for the static Einstein-Maxwell equations representing the exterior gravitational field of a massive magnetic dipole are derived. They are then used for construction of the stationary electrovacuum solutions reducing to the Schwarzschild metric in a pure vacuum limit.     

Interaction of plasma clusters with an axially symmetric magnetic field

The paper reports about measurements of the magnetic flux of a probe coil excited by a plasma cluster, moving in an axially symmetric magnetic field. The effective diamagnetic current, inductance and resistance of the cluster are derived from the dependence of the measured flux on the distance between the standard coil and the coil forming the magnetic field, as well as from the estimated main dimensions of the cluster.In conclusion the author wishes to express his thanks to Mr. J. Divíek for his devoted work in assembling the apparatus and to Mr, J. Bacílek for his work connected with the vacuum technique.     

On the linearization of source free gauge field equations

A scheme for linearizing the source free Yang-Mills field equations is given. An infinite parameter invariance group of the gauge field equations is discovered.     

On axially symmetric soliton solutions of the coupled scalar-vector-tensor equations in general relativity

The inverse scattering theory used by Belinsky and Zakharov to obtain soliton solutions of the of the Einstein equations is here applied to the case of a five-dimensional space and interpreted in the framework of the Jordan-Kaluza-Klein theory. For two solitons exact, stationary, axially symmetric and asymptotically flat solutions are obtained.     

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.