On spherically symmetric fields in gauge theories

Gauge fields admitting spherical symmetry are listed. Spherically symmetric solutions of Yang-Mills equations and spherically symmetric magnetic monopoles are studied. A simple exact solution of the Yang-Mills and Einstein equations is found.     

Elliptic-type solutions to the scale invariant Yang-Mills and sigma-model hierarchies

We outline the construction of non-self-dual elliptic solutions by relating the spherically symmetric subsystem of the (scale invariant) Yang-Mills and sigmamodel hierarchies to the hierarchies of ⁴ and Sine-Gordon models in one dimension respectively. The construction is carried out explicitly for the usual Yang-Mills model on ₄, and the first two sigma-models on ₂ and ₄. The solution to the first member of the Yang-Mills hierarchy is related to elliptic solutions found previously.     

Static spherically symmetric solutions of the classical Yang-Mills equations

All spherically symmetric solutions with time-independent fields are found for the classical Yang-Mills equations with an extended charge in the case of the SU(2) gauge group. There is a physically different solution corresponding to each choice of an arbitrary function of radius. In all solutions the energy and the charge are reduced compared to the Coulomb solution. For certain solutions the reduced charge and all fields outside the source vanish.     

Self-consistent spherically symmetric solutions of the Yang-Mills-Dirac-equations

TheSU(2) Yang-Mills equations coupled self-consistently to an isospin 1/2-Dirac equation are studied. Static spherically symmetric exact analytic solutions are given. They all share the property of infinite energy.     

Bäcklund transformations and exact solutions of the stationary axially symmetric Einstein equations

The Bäcklund transformations of the self-dual Yang-Mills fields are used to derive exact solutions of the stationary axially symmetric Einstein equations. Three solutions which belong to an infinite series of such solutions are explicitly calculated, the first of which is the Lewis solution. Also the first of another infinite series of solutions is calculated, which for some value of a parameter becomes the Papapetrou solution.     

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.     

Invariant Solutions of the Yang–Mills Field Equations Coupled to a Scalar Doublet

The Yang–Mills system of field equations which includes coupling to an SU(2) scalar matter doublet is developed. It is shown that an SU(2) current for a scalar matter doublet can be developed. The basic structure which fits the Yang–Mills system is somewhat different from the case of the scalar triplet. Using this form for the scalar current, it is possible to write down the Yang–Mills system which couples to the scalar matter doublet. It is shown that several sets of solutions to this system of equations can be obtained.     

Static,Spherically Symmetric Solutions of Yang-Mills-Dilaton Theory

Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally regular solutions further distinguished by the number of nodes of their Yang-Mills potential. The third class consists of oscillating solutions playing the role of limits of regular solutions, when the number of nodes tends to infinity. We show that all three sets of solutions are non-empty. Furthermore we give asymptotic formulae for the parameters of regular solutions and confront them with numerical results.     

Part 1 : Topological aspects of Yang-Mills fields in curved spaces. (Exact solutions)

To explore in its full richness the topological possibilities of gauge fields one should allow for simultaneous presence of gravitational and Yang-Mills ones. Thus if the integral topological indices of the Yang-Mills field for a flat Euclidean base space is associated with the structure of the vacuum, one may ask among other questions of interest, how this spectrum might be modified when the base space itself has non trivial indices. Exact solutions of SU(2) Yang-Mills fields are presented for metrics corresponding to well-known gravitational instantons. Such selfdual solutions, with vanishing energy monien-tunl tensor T_μv for Euclidean signature of the base space, do not perturb the metric. Thus they provide solutions of the combined gravitational-Y.M. system. New topological possibilities, such as finite action SU(2) fields with fractional indices for many centre inetrics are displayed explicitly. As another type of possibility non selfdual, finite action solutions are constructed explicitly on Schwarzschild and de Sitter metrics, the solution being real in the first and complex in second case respectively. It is also shown how various meron type solutions in flat space can be derived systematically from a very simple static solution in de Sitter.     

Pulsed EPR study on large dynamic electron polarisation created in the quenching of photo-excited xanthene dyes by nitroxide radicals in aqueous solutions

Dynamic electron polarisation (DEP) produced by the quenching of dye molecules in the triplet excited states by nitroxide radicals was investigated in aqueous solutions by pulsed electron paramagnetic resonance and transient absorption spectroscopy. An analysis of the measured quenching rate constants suggests that quenching is promoted by either exchange or charge-transfer mechanisms for a triplet dye and a doublet radical pair. An unusually large DEP on the radical was found generated in the nitroxide and Eosin Y or Rose Bengal systems in aqueous solutions. Quantitative analysis indicates that the DEP values in aqueous solutions range from ?40 to ?150 in the unit of thermal spin polarisation, which is in contrast to previously reported small DEP values of less than ?10 for organic triplet molecules in benzene solutions [22–27,29,31,32]. From the theoretical analysis of DEP, an origin of this large DEP was attributed to the notably slow diffusion motion of Eosin Y and Rose Bengal in water.     

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.     

Gauge cosmic chiral strings in general relativity

Cylindrically symmetric self-gravitating configurations of string (vortex) type are considered within the framework of the chiral SU(2) model with the inclusion of the Yang-Mills proper gauge field. In the approximation of the large topological charge n the solutions to the field equations are found, with the magnetic field of the vortex being longitudinal. The linear energy density of the vortex configuration is estimated. The text was submitted by the author in English.     

Self dual solutions of the temperature SU(2) Yang-Mills theory

Continuing previous work we elaborate on the method of “heating” the self-dual axially symmetric fields of the SU(2) Yang-Mills theory to finite temperature. Heating consists of performing—in certain Ansatz functions which are two-dimensional (2D) conformally invariant—a 2D conformal transformation x = x₀ + i ∥x∥ → y(x), where the analytic function y(x) is periodic in the Euclidean time variable x₀. Solutions are preserved by this manipulation, which automatically changes zero-temperature fields into finite temperature ones. One can exploit this simple fact in various ways. The Harrington-Shepard caloron solution of the temperature Yang-Mills theory can be gotten from the T = 0 instanton by the transformation y(x) = (πT)^?1 tan πTx. One can generate a multicaloron solution from the T = 0 one instanton solution by a conformal transformation. Generally, self-dual axially symmetric Yang-Mills fields can be heated without spoiling self duality. The caloron and three other temperature solutions are studied in some detail. One of the new solutions is a generalized caloron with interesting properties. Our study reveals a remarkable property of the self-dual sector of the temperature Yang-Mills theory: it is full of Wu-Yang (color) monopoles at high temperature. At low temperature these monopoles disappear.     

Fictitious Yang-Mills fields in a plane symmetric universe

It is shown that if we apply the Ansatz recently proposed by Oh and Teh to find a static Yang-Mills field in a plane symmetric universe, we get simply the vacuum Taub solution or the maxwellian Patnaik solution. In addition, we have shown that there are no plane wave solutions.     

Time-resolved EPR spectra of a photoexcited phenanthrene-linked copper(II)-free-base porphyrin dimer: An intermediate-coupling case in a triplet-doublet spin system

Time-resolved electron paramagnetic resonance (TREPR) spectra are presented for a phenanthrene-linked copper(II)-free-base porphyrin dimer. In the lowest electronic excited state, the free-base half is in the (π, π*) triplet state and the copper-porphyrin half is in the doublet ground state due to the copper(II) spin. Because of the interaction between the triplet and doublet spins, the excited state of the dimer is described as a coupled triplet-doublet pair state. By choosing the excitation wavelength, this coupled state is produced via either the intersystem crossing within the free base or the energy transfer from the excited state of the copper porphyrin. The observed TREPR spectra show very large spectral widths compared to that of the triplet state in the free-base monomer. In addition, there is a prominent absorptive band in the center of the spectra regardless of the generation pathway. These features can be interpreted as characteristic properties in an intermediate-coupling case, where the degree of the triplet and doublet mixing largely depends on the molecular orientation relative to the magnetic field.     

O(3) symmetric merons in an SU(3) Yang-Mills theory

We investigate irreducible, O(3) symmetric multiple-meron solutions to the classical SU(3) Yang-Mills equations in four-dimensional Euclidean space. The solutions have topological charge density equal to a sum of delta-functions with integer coefficients, and correspond to solutions of a system of two coupled singular elliptic equations. We prove the existence of twomeron solutions of the coupled system.Supported in part by the National Science Foundation under Grant No. PHY77-18762.     

Magnetic monopole in the general theory of relativity

Equations of motion are obtained for Yang-Mills and Higgs fields using the Georgi-Glashow SO(3)-model in a curved spherically symmetric space-time. Magnetic monopole and dion solutions and the space-time metric are found in the intrinsic gravitational field. A particlelike solution of the magnetic monopole and dion type is constructed in the external field of a static universe in the Bogomol'nyi-Prasad-Sommerfield limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 89–93, November, 1982.     

Locally symmetric riemannian spaces and solutions of Yang-Mills equations

We give an explicit construction for all classical solutions of Euclidean SU(2) Yang-Mills equations which can be obtained by reduction of conformally flat locally symmetric Riemannian spaces.Address after 1 April 1987: Institut für Theoretische Physik, Universität Karlsruhe, D-7500 Karlsruhe 1, West Germany.