A novel strong coupling expansion of the QCD Hamiltonian

Introducing an infinite spatial lattice with box length a, a systematic expansion of the physical QCD Hamiltonian in \lambda = g^{-2/3} can be obtained. The free part is the sum of the Hamiltonians of the quantum mechanics of spatially constant fields for each box, and the interaction terms proportional to \lambda^n contain n discretised spatial derivatives connecting different boxes. As an example, the energy of the vacuum and the lowest scalar glueball is calculated up to order \lambda^2 for the case of SU(2) Yang-Mills theory.Comment: Talk given at the 6th International Workshop on "Critical Point and Onset of Deconfinement (CPOD)", Dubna, Russia, 23-29 August 201

Representations of Uh(su(N))U_h(su(N)) derived from quantum flag manifolds

A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left \Uh -- module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of Leibniz rule. Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occuring in the diagonalization one can extract finite-dimensional irreducible representations of \Uh as cyclic submodules.Comment: LaTeX file, JMP (to appear

Testing Gaussian random hypothesis with the cosmic microwave background temperature anisotropies in the three-year WMAP data

We test the hypothesis that the temperature of the cosmic microwave background is consistent with a Gaussian random field defined on the celestial sphere, using de-biased internal linear combination (DILC) map produced from the 3-year WMAP data. We test the phases for spherical harmonic modes with l <= 10 (which should be the cleanest) for their uniformity, randomness, and correlation with those of the foreground templates. The phases themselves are consistent with a uniform distribution, but not for l <= 5, and the differences between phases are not consistent with uniformity. For l=3 and l=6, the phases of the CMB maps cross-correlate with the foregrounds, suggestion the presence of residual contamination in the DLC map even on these large scales. We also use a one-dimensional Fourier representation to assemble a_lm into the \Delta T_l(\phi) for each l mode, and test the positions of the resulting maxima and minima for consistency with uniformity randomness on the unit circle. The results show significant departures at the 0.5% level, with the one-dimensional peaks being concentrated around \phi=180 degs. This strongly significant alignment with the Galactic meridian, together with the cross-correlation of DILC phases with the foreground maps, strongly suggests that even the lowest spherical harmonic modes in the map are significantly contaminated with foreground radiation.Comment: submitted to ApJL, one paragraph is added in Section 3 and some more in the Referenc

Electromagnetic field near cosmic string

The retarded Green function of the electromagnetic field in spacetime of a straight thin cosmic string is found. It splits into a geodesic part (corresponding to the propagation along null rays) and to the field scattered on the string. With help of the Green function the electric and magnetic fields of simple sources are constructed. It is shown that these sources are influenced by the cosmic string through a self-interaction with their field. The distant field of static sources is studied and it is found that it has a different multipole structure than in Minkowski spacetime. On the other hand, the string suppresses the electric and magnetic field of distant sources--the field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two references added, typos correcte

Squeezed Gluon Condensate and Quark Confinement in the Global Color Model of QCD

We discuss how the presence of a squeezed gluon vacuum might lead to quark confinement in the framework of the global colour model of QCD. Using reduced phase space quantization of massive vector theory we construct a Lorentz invariant and colourless squeezed gluon condensate and show that it induces a permanent, nonlocal quark interaction (delta-function in 4-momentum space), which according to Munczek and Nemirovsky might lead to quark confinement. Our approach makes it possible to relate the strength of this effective confining quark interaction to the strength of the physical gluon condensate.Comment: 18 pages LaTeX, to appear in Int. J. Mod. Phys.

Pancreatic islets communicate with lymphoid tissues via exocytosis of insulin peptides.

Tissue-specific autoimmunity occurs when selected antigens presented by susceptible alleles of the major histocompatibility complex are recognized by T cells. However, the reason why certain specific self-antigens dominate the response and are indispensable for triggering autoreactivity is unclear. Spontaneous presentation of insulin is essential for initiating autoimmune type 1 diabetes in non-obese diabetic mice1,2. A major set of pathogenic CD4 T cells specifically recognizes the 12-20 segment of the insulin B-chain (B:12-20), an epitope that is generated from direct presentation of insulin peptides by antigen-presenting cells3,4. These T cells do not respond to antigen-presenting cells that have taken up insulin that, after processing, leads to presentation of a different segment representing a one-residue shift, B:13-214. CD4 T cells that recognize B:12-20 escape negative selection in the thymus and cause diabetes, whereas those that recognize B:13-21 have only a minor role in autoimmunity3-5. Although presentation of B:12-20 is evident in the islets3,6, insulin-specific germinal centres can be formed in various lymphoid tissues, suggesting that insulin presentation is widespread7,8. Here we use live imaging to document the distribution of insulin recognition by CD4 T cells throughout various lymph nodes. Furthermore, we identify catabolized insulin peptide fragments containing defined pathogenic epitopes in β-cell granules from mice and humans. Upon glucose challenge, these fragments are released into the circulation and are recognized by CD4 T cells, leading to an activation state that results in transcriptional reprogramming and enhanced diabetogenicity. Therefore, a tissue such as pancreatic islets, by releasing catabolized products, imposes a constant threat to self-tolerance. These findings reveal a self-recognition pathway underlying a primary autoantigen and provide a foundation for assessing antigenic targets that precipitate pathogenic outcomes by systemically sensitizing lymphoid tissues

Design of arbitrary optical filters in silicon-on-insulator using evanescently-coupled Bragg gratings

Spectral filters are experiencing an increasing demand in several applications of the silicon- on-insulator (SOI) platform. Many works have demonstrated that arbitrary frequency responses can be synthesized by apodizing the coupling coefficient profile of an integrated Bragg grating. However, the high index contrast of the SOI platform hinders their practical implementation, due to the difficulty of achieving the precise control required in the Bragg strength. In this paper, we propose the implementation of spectral filters using an architecture based on placing loading segments within the evanescent field region of a photonic wire waveguide. The Bragg coupling coefficient can be accurately controlled by simply moving the segments away from, or closer to, the waveguide core. The layerpeeling algorithm, in conjunction with a Floquet-Bloch modal analysis, allows to determine the spatial distribution of the segments that synthesizes the desired spectrum. The proposed topology is verified by designing a filter with five arbitrary passbands.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Lie group analysis of a generalized Krichever-Novikov differential-difference equation

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension 1 \le \mbox{dim}L \le 5. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies \mbox{dim}L=2. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations