Realisation of chiral symmetry in the domain model of QCD

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background domain-like gluon field. Quark fluctuations satisfy a chirality violating boundary conditions parametrized by a random chiral angle $\alpha_j$ on the $j-th$ domain. The free energy of an ensemble of $N\to\infty$ domains depends on $\{\alpha_j, j=1... N\}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial U(1) degeneracy in the ground state, leaving only a residual axial Z(2) symmetry. This discrete symmetry and flavour $SU(N_f)_L\times SU(N_f)_R$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of Dirac operator. In order to illustrate the splitting between the $\eta'$ from octet pseudoscalar mesons realised in the domain model, we estimate the masses of light pseudoscalar and vector mesons.Comment: 27 pages, uses RevTeX, 3 figures. v.2. includes additional references and comment

Model for SU(3) vacuum degeneracy using light-cone coordinates

Working in light-cone coordinates, we study the zero-modes and the vacuum in a 2+1 dimensional SU(3) gauge model. Considering the fields as independent of the tranverse variables, we dimensionally reduce this model to 1+1 dimensions. After introducing an appropriate su(3) basis and gauge conditions, we extract an adjoint field from the model. Quantization of this adjoint field and field equations lead to two constrained and two dynamical zero-modes. We link the dynamical zero-modes to the vacuum by writing down a Schrodinger equation and prove the non-degeneracy of the SU(3) vacuum provided that we neglect the contribution of constrained zero-modes.Comment: 22 pages, 5 figure

On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation

SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction. On the light-cone, the vacuum structure of this theory is encoded in the dynamical zero mode of a gluon and a constrained mode of the scalar field. The latter satisfies a linear constraint, suggesting no nontrivial vacua in the present paradigm for symmetry breaking on the light-cone. I develop a diagrammatic method to solve the constraint equation. In the adiabatic approximation I compute the quantum mechanical potential governing the dynamical gauge mode. Due to a condensation of the lowest omentum modes of the dynamical gluons, a centrifugal barrier is generated in the adiabatic potential. In the present theory however, the barrier height appears too small to make any impact in this odel. Although the theory is superrenormalisable on naive powercounting grounds, the removal of ultraviolet divergences is nontrivial when the constrained mode is taken into account. The open aspects of this problem are discussed in detail.Comment: LaTeX file, 26 pages. 14 postscript figure

Quantum Electrodynamics in the Light-Front Weyl Gauge

We examine QED(3+1) quantised in the `front form' with finite `volume' regularisation, namely in Discretised Light-Cone Quantisation. Instead of the light-cone or Coulomb gauges, we impose the light-front Weyl gauge $A^-=0$. The Dirac method is used to arrive at the quantum commutation relations for the independent variables. We apply `quantum mechanical gauge fixing' to implement Gau{\ss}' law, and derive the physical Hamiltonian in terms of unconstrained variables. As in the instant form, this Hamiltonian is invariant under global residual gauge transformations, namely displacements. On the light-cone the symmetry manifests itself quite differently.Comment: LaTeX file, 30 pages (A4 size), no figures. Submitted to Physical review D. January 18, 1996. Originally posted, erroneously, with missing `Weyl' in title. Otherwise, paper is identica

Neutral pion decay in dense skyrmion matter

We study the density dependence of the decay $\pi^0\to \gamma \gamma$ using the Skyrme Lagrangian to describe simultaneously both the matter background and mesonic fluctuations. Pion properties such as mass and decay constant are modified by the medium. This leads to large suppression at high density of both photo-production from the neutral pion and the reverse process. The in-medium effective charge of $\pi^{\pm}$ are also discussed in the same framework.Comment: 8 pages, 4 figures. Corrections in light of referee comment

Weyl group, CP and the kink-like field configurations in the effective SU(3) gauge theory

Effective Lagrangian for pure Yang-Mills gauge fields invariant under the standard space-time and local gauge SU(3) transformations is considered. It is demonstrated that a set of twelve degenerated minima exists as soon as a nonzero gluon condensate is postulated. The minima are connected to each other by the parity transformations and Weyl group transformations associated with the color su(3) algebra. The presence of degenerated discrete minima in the effective potential leads to the solutions of the effective Euclidean equations of motion in the form of the kink-like gauge field configurations interpolating between different minima. Spectrum of charged scalar field in the kink background is discussed.Comment: 10 pages, 1 figure, added references for sections 1 and

Multispectral pattern recognition reveals a diversity of clinical signs in intermediate age-related macular degeneration

PURPOSE. To develop a proof-of-concept, computational method for the quantification and classification of fundus images in intermediate age-related macular degeneration (AMD). METHODS. Multispectral, unsupervised pattern recognition was applied to 184 fundus images from 10 normal and 36 intermediate AMD eyes. The imaging results of preprocessed, grayscale images from three modalities (infrared, green, and fundus autofluorescence scanning laser ophthalmoscopy) were automatically classified into various clusters sharing a common spectral signature, using a k-means clustering algorithm. Class separability was calculated by using transformed divergence (DT). The classification results for large drusen, pigmentary abnormalities, and areas unaffected by AMD were compared against three expert observers for concordance, and to calculate sensitivity and specificity. RESULTS. Multispectral, unsupervised pattern recognition successfully identified a finite number of AMD-specific, statistically separable signatures in eyes with intermediate AMD. By using a correct classification criterion of >83% for identical clusters and a total of 1693 expert annotations, the sensitivity and specificity of multispectral pattern recognition for the detection of AMD lesions was 74% and 98%, respectively. Large drusen and pigmentary abnormalities were correctly classified in 75% and 68% of instances, respectively. CONCLUSIONS. We describe herein a novel approach for the classification of multispectral images in intermediate AMD. Automated classification of intermediate AMD, using multispectral pattern recognition, has moderate sensitivity and high specificity, when compared against clinical experts. The methods described may have a future role in AMD screening or monitoring

Towards Solving QCD - The Transverse Zero Modes in Light-Cone Quantization

We formulate QCD in (d+1) dimensions using Dirac's front form with periodic boundary conditions, that is, within Discretized Light-Cone Quantization. The formalism is worked out in detail for SU(2) pure glue theory in (2+1) dimensions which is approximated by restriction to the lowest {\it transverse} momentum gluons. The dimensionally-reduced theory turns out to be SU(2) gauge theory coupled to adjoint scalar matter in (1+1) dimensions. The scalar field is the remnant of the transverse gluon. This field has modes of both non-zero and zero {\it longitudinal} momentum. We categorize the types of zero modes that occur into three classes, dynamical, topological, and constrained, each well known in separate contexts. The equation for the constrained mode is explicitly worked out. The Gauss law is rather simply resolved to extract physical, namely color singlet states. The topological gauge mode is treated according to two alternative scenarios related to the In the one, a spectrum is found consistent with pure SU(2) gluons in (1+1) dimensions. In the other, the gauge mode excitations are estimated and their role in the spectrum with genuine Fock excitations is explored. A color singlet state is given which satisfies Gauss' law. Its invariant mass is estimated and discussed in the physical limit.Comment: LaTex document, 26 pages, one figure (obtainable by contacting authors). To appear in Physical. Review

Dimensional renormalization: ladders to rainbows

Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive factors and renormalized Green functions to all orders in perturbation theory for rainbow graphs and vertex (or scattering diagrams) at zero momentum transfer, in the context of dimensional renormalization, and we prove that the correct anomalous dimensions for those processes emerge in the limit D -> 4.Comment: RevTeX, no figure