Yang-Mills Field Configurations Research Articles

YANG-MILLS CONDENSATES IN COSMOLOGY

We discuss homogeneous and isotropic cosmological models driven by SU(2) gauge fields in the framework of Einstein gravity. There exists a Yang-Mills field configuration, parametrized by a single scalar function, which consists of parallel electric and magnetic fields and has the stress tensor mimicking an homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous symmetry breaking sharing the same property is the Yang-Mills coupled to the complex doublet Higgs, this exists only in the case of the closed universe. This model contains an intrinsic mechanism for inflation due to the Higgs potential. Our second goal is to show that a successful inflation can be achieved also within the pure Yang-Mills theory adding an appropriate theta-term.

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.

Dirac-Yang monopoles in all dimensions and their regular counterparts

The Dirac-Yang monopoles are singular Yang-Mills field configurations in all Euclidean dimensions. The regular counterpart of the Dirac monopole in D = 3 is the’ t Hooft-Polyakov monopole, the former being simply a gauge transform of the asymptotic fields of the latter. Here, regular counterparts of Dirac-Yang monopoles in all dimensions are described. In the first part of this work, the hierarchy of Dirac-Yang monopoles will be defined; in the second part, the motivation to study these in a topical context will be briefly presented; and in the last part, two classes of regular counterparts to the Dirac-Yang hierarchy will be presented.

Quasi-local holography and quasi-local mass of classical fields in Minkowski spacetime

The 2-surface characterization of special classical radiative Higgs, Yang–Mills and linear zero-rest-mass fields with any spin is investigated. We determine all the zero quasi-local mass Higgs and Yang–Mills field configurations with compact semi-simple gauge groups, and show that they are plane waves (provided the Higgs field is massless and linear) and appropriate generalizations of plane waves (‘Yang–Mills pp-waves’), respectively. A tensor field (generalizing the energy–momentum tensor for the Maxwell field and of the Bel–Robinson tensor for the linearized gravitational field) is found by means of which the pp-wave nature of the solutions of the linear zero-rest-mass field equations with any spin can be characterized equivalently. It is shown that these radiative Yang–Mills and linear zero-rest-mass fields, given on a finite globally hyperbolic domain D, are determined completely by certain unconstrained data set on a closed spacelike 2-surface, the ‘edge of D’. These pure radiative solutions are shown to determine a dense subset in the set of all continuous fields. Thus for these fields some ‘classical quasi-local holography’ holds.

Perturbative construction of self-dual configurations on the torus

We develop a perturbative expansion which allows the construction of non-abelian self-dual SU(2) Yang-Mills field configurations on the four-dimensional torus with topological charge 1/2. The expansion is performed around the constant field strength abelian solutions found by 't Hooft. Next to leading order calculations are compared with numerical results obtained with lattice gauge theory techniques.

Chaotic behavior of confining lattice Gauge field configurations

We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.

Quantum cosmological multidimensional Einstein-Yang-Mills model in anR×S3×Sdtopology

The quantum cosmological version of the multidimensional Einstein-Yang-Mills model in an $\mathbf{R}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{d}$ topology is studied in the framework of the Hartle-Hawking proposal. In contrast with previous work in the literature, we consider Yang-Mills field configurations with nonvanishing time-dependent components in both ${S}^{3}$ and ${S}^{d}$ spaces. We obtain stable compactifying solutions that do correspond to extrema of the Hartle-Hawking wave function of the Universe. Subsequently, we also show that the regions where the 4-dimensional metric behaves classically or quantum mechanically (i.e., regions where the metric is Lorentzian or Euclidean) will depend on the number $d$ of compact space dimensions.

String theory and cosmology

We discuss the main cosmological implications of considering string-loop effects and a potential for the dilaton in the lowest order string effective action. Our framework is based on the effective model arising from regarding homogeneous and isotropic dilaton, metric and Yang-Mills field configurations. The issues of inflation, entropy crisis and the Polonyi problem as well as the problem of the cosmological constant are discussed.

General cosmological features of the Einstein-Yang-Mills-dilaton system in string theories

We establish the main features of homogeneous and isotropic dilation, metric and Yang-Mills field configurations in a cosmological framework. We discuss the way inflationary solutions can be obtained for a quadratic dilaton potential. Special attention is paid to the energy exchange between the dilaton and the Yang-Mills field and, in particular, a new energy exchange term is identified which may lead to a possible solution of the Polonyi problem in 4-dimensional string models and in dynamical supersymmetry breaking scenarios.

The geometry of inequivalent quantizations

We describe how inequivalent quantizations (superselection sectors) arise within two related algebraic approaches to quantum mechanics (viz. quantization by canonical groups and by C ∗-algebras). By construction of the quantum hamiltonian and the path integral of a particle moving on a coset space, we show that the inequivalent quantizations manifest themselves as the particle coupling to a certain fictitious external gauge field, in a representation depending on the superselection sector; various well-known topologically non-trivial Yang-Mills field configurations emerge in this way. The general theory is illustrated by taking the coset space to be a circle and a sphere, which puts θ-angles (hence the Aharonov-Bohm effect) and the Dirac charge quantization condition, respectively, in a new light.

Analytic solutions of the SU(3) Yang–Mills field equations with external sources

For external sources specified in the radial gauge frame, it is demonstrated how the SU(3) Yang–Mills field configuration can be constructed from the SU(2) solutions. This is explicitly illustrated for the type-II solutions that exhibit the bifurcation phenomenon.

Compactifications of N = 1, D = 10 supergravity to 2 and 3 dimensions

Utilizing Killing spinors on spheres we show that N = 1, D = 10 supergravity admits compactifications to d = 2 and 3, which are: AdS 3 × S 7, AdS 3 × S 1 × S 6, AdS 3 × S 1 × S 3 × S 3, AdS 2 × S 8, AdS 2 × SU(3). In all these solutions the Yang-Mills field configuration is non-vanishing, and supersymmetry is broken.

Yang-Mills field configurations with critical source strengths

A new class of type-I solutions of the Yang-Mills field equations is derived. This class of solutions exists only if the external source strengths exceed certain critical values although it has the same boundary conditions at the origin as at infinity.

Euclidean self-dual yang-mills field configurations

The determination of a large class of regular and singular Euclidean self-dual Yang-Mills field configurations is reduced to the solution of a set of linear algebraic equations. The matrix of the coefficients is a polynomial functions ofx and the rules for its construction are elementary.

Conservation-law violation at high energy by anomalies

The time evolution of a quantum Fermi field is investigated in the background of a Minkowski-space, Yang-Mills field configuration with nonvanishing topological charge. The Fermi system is assumed to possess a current ${j}_{\ensuremath{\mu}}(x)$ conserved up to an axial-vector anomaly: ${\ensuremath{\partial}}^{\ensuremath{\mu}}{j}_{\ensuremath{\mu}}=(\frac{{g}^{2}}{32{\ensuremath{\pi}}^{2}}){N}_{\mathrm{ij}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}^{i}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}^{j\ensuremath{\mu}\ensuremath{\nu}}$. It is shown explicitly that the time-dependent Yang-Mills field ${A}_{\ensuremath{\mu}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},t)$ creates and destroys fermions in such a way that the total fermionic charge $\ensuremath{\int}{j}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},t){d}^{3}x$ present in the final state differs from that in the initial state by precisely the amount predicted by the anomaly equation. If ${A}_{\ensuremath{\mu}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},t)$ approaches a gauge transformation sufficiently rapidly for large $t$, this change in charge can be identified with the number of zero crossings present in the energy spectrum of the time-dependent Dirac Hamiltonian. Finally, it is demonstrated that the change in the charge carried by the fermions will differ from that predicted by the axial-vector anomaly if the large-time limit of ${A}_{\ensuremath{\mu}}$ contains physical radiation.

Dense and dilute instanton-anti-instanton pair configurations

We present a Yang-Mills gauge field configuration which for large values of a separation parameter is an instanton-anti-instanton pair. At a minimum finite separation the field is a pure gauge. The interaction is calculated for large and small separations. According to an approximation algorithm the configuration is the most important quantum fluctuation about the exact solutions.

Static sources in classical Yang-Mills theory

We examine initial-time Yang-Mills field configurations which satisfy Gauss's law in the presence of static external sources. We show that if such a configuration is an extremum of the energy, then it is a static solution of the Yang-Mills equations. Next we consider Yang-Mills field configurations which satisfy Gauss's law for one external point source. We show that there exists a large class of such configurations which have lower energy than the Coulomb solution.