Loop Representations for 2+1 Gravity on a Torus

We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this system. In particular, we look at the loop transform in the part of the phase space where the holonomies are boosts and study its kernel. This kernel is dense in the connection representation and the transform is not continuous with respect to the natural topologies, even in its domain of definition. Nonetheless, loop representations isomorphic to the connection representation corresponding to this part of the phase space can still be constructed if due care is taken. We present this construction but note that certain ambiguities remain; in particular, functions of loops cannot be uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-

Classical Loop Actions of Gauge Theories

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.Comment: LaTeX 14 page

Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles be quantized. On the other hand, in the Maxwell case, we find that charge quantization is necessary in order to the geometric representation be consistent.Comment: 6 pages, improved versio

The large cosmological constant approximation to classical and quantum gravity: model examples

We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens several questions about how relevant the results produced can possibly be. Among the questions is the issue of how useful are results for large values of the cosmological constant and how the approach can deal with several pathologies that are expected to be present in the canonical approach to quantum gravity. With the aim of clarifying these points, and to make our construction as explicit as possible, we study its application in several simple models. We consider Bianchi cosmologies, the asymmetric top, the coupled harmonic oscillators with constant energy density and a simple quantum mechanical system with two Hamiltonian constraints. We find that the technique satisfactorily deals with the pathologies of these models and offers promise for finding (at least some) results even for small values of the cosmological constant. Finally, we briefly sketch how the method would operate in the full four dimensional quantum general relativity case.Comment: 21 pages, RevTex, 2 figures with epsfi

Superheating fields of superconductors: Asymptotic analysis and numerical results

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\rm sh}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of $\kappa^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa<0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.Comment: 14 pages, 8 uuencoded figures, Revtex 3.

Tumor Necrosis Factor - Related Apoptosis-Inducing Ligand (TRAIL) promotes angiogenesis and ischemia- induced neovascularization via NADPH Oxidase 4 (NOX4) and Nitric Oxide - dependent mechanisms

Background — Tumor necrosis factor–related apoptosis-inducing ligand (TRAIL) has the ability to inhibit angiogenesis by inducing endothelial cell death, as well as being able to promote pro- angiogenic activity in vitro. These seemingly opposite effects make its role in ischemic disease unclear. Using Trail_/_ and wildtype mice, we sought to determine the role of TRAIL in angiogenesis and neovascularization following hindlimb ischemia. Methods and Results — Reduced vascularization assessed by real-time 3-dimensional Vevo ultrasound imaging and CD31 staining was evident in Trail_/_ mice after ischemia, and associated with reduced capillary formation and increased apoptosis. Notably, adenoviral TRAIL administration significantly improved limb perfusion, capillary density, and vascular smooth-muscle cell content in both Trail_/_ and wildtype mice. Fibroblast growth factor-2, a potent angiogenic factor, increased TRAIL expression in human microvascular endothelial cell-1, with fibroblast growth factor-2-mediated proliferation, migration, and tubule formation inhibited with TRAIL siRNA. Both fibroblast growth factor-2 and TRAIL significantly increased NADPH oxidase 4 (NOX4) expression. TRAIL-inducible angiogenic activity in vitro was inhibited with siRNAs targeting NOX4, and consistent with this, NOX4 mRNA was reduced in 3-day ischemic hindlimbs of Trail_/_ mice. Furthermore, TRAIL-induced proliferation, migration, and tubule formation was blocked by scavenging H2O2, or by inhibiting nitric oxide synthase activity. Importantly, TRAIL-inducible endothelial nitric oxide synthase phosphorylation at Ser-1177 and intracellular human microvascular endothelial cell-1 cell nitric oxide levels were NOX4 dependent. Conclusions — This is the first report demonstrating that TRAIL can promote angiogenesis following hindlimb ischemia in vivo. The angiogenic effect of TRAIL on human microvascular endothelial cell-1 cells is downstream of fibroblast growth factor-2, involving NOX4 and nitric oxide signaling. These data have significant therapeutic implications, such that TRAIL may improve the angiogenic response to ischemia and increase perfusion recovery in patients with cardiovascular disease and diabetes

A Geometric Approach to Massive p-form Duality

Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.Comment: 26 pages, LaTeX. The discussion about the equivalence between the Proca model and two seldual models, with opposite spins, was eliminated. Typos correcte

Integration of optical telecommunications and radio access networks to assure quality of service

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Nonminimal Couplings in the Early Universe: Multifield Models of Inflation and the Latest Observations

Models of cosmic inflation suggest that our universe underwent an early phase of accelerated expansion, driven by the dynamics of one or more scalar fields. Inflationary models make specific, quantitative predictions for several observable quantities, including particular patterns of temperature anistropies in the cosmic microwave background radiation. Realistic models of high-energy physics include many scalar fields at high energies. Moreover, we may expect these fields to have nonminimal couplings to the spacetime curvature. Such couplings are quite generic, arising as renormalization counterterms when quantizing scalar fields in curved spacetime. In this chapter I review recent research on a general class of multifield inflationary models with nonminimal couplings. Models in this class exhibit a strong attractor behavior: across a wide range of couplings and initial conditions, the fields evolve along a single-field trajectory for most of inflation. Across large regions of phase space and parameter space, therefore, models in this general class yield robust predictions for observable quantities that fall squarely within the "sweet spot" of recent observations.Comment: 17pp, 2 figs. References added to match the published version. Published in {\it At the Frontier of Spacetime: Scalar-Tensor Theory, Bell's Inequality, Mach's Principle, Exotic Smoothness}, ed. T. Asselmeyer-Maluga (Springer, 2016), pp. 41-57, in honor of Carl Brans's 80th birthda