Noncommutative Gauge Theory on the q-Deformed Euclidean Plane

In this talk we recall some concepts of Noncommutative Gauge Theories. In particular, we discuss the q-deformed two-dimensional Euclidean Plane which is covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map is constructed to express noncommutative fields in terms of their commutative counterparts.Comment: 5 pages; Talk given by Frank Meyer at the 9th Adriatic Meeting, September 4th-14th, 2003, Dubrovni

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Black Hole Production at the Large Hadron Collider

Black hole production at the Large Hadron Collider (LHC) is an interesting consequence of TeV-scale gravity models. The predicted values, or lower limits, for the fundamental Planck scale and number of extra dimensions will depend directly on the accuracy of the black hole production cross-section. We give a range of lower limits on the fundamental Planck scale that could be obtained at LHC energies. In addition, we examine the effects of parton electric charge on black hole production using the trapped-surface approach of general relativity. Accounting for electric charge of the partons could reduce the black hole cross-section by one to four orders of magnitude at the LHC.Comment: CTP Symposium on Supersymmetry at LHC: Theoretical and Experimental Perspectives at the British University in Egypt 11-14 March 200

On The Interaction Of D0-Brane Bound States And RR Photons

We consider the problem of the interaction between D0-brane bound state and 1-form RR photons by the world-line theory. Based on the fact that in the world-line theory the RR gauge fields depend on the matrix coordinates of D0-branes, the gauge fields also appear as matrices in the formulation. At the classical level, we derive the Lorentz-like equations of motion for D0-branes, and it is observed that the center-of-mass is colourless with respect to the SU(N) sector of the background. Using the path integral method, the perturbation theory for the interaction between the bound state and the RR background is developed. We discuss what kind of field theory may be corresponded to the amplitudes which are calculated by the perturbation expansion in world-line theory. Qualitative considerations show that the possibility of existence of a map between the world-line theory and the non-Abelian gauge theory is very considerable.Comment: LaTeX, 28 pages, 4 eps figures. v2 and v3: eqs. (3.18) and (B.2) are corrected, very small change

Black Hole Cross Section at the Large Hadron Collider

Black hole production at the Large Hadron Collider (LHC) was first discussed in 1999. Since then, much work has been performed in predicting the black hole cross section. In light of the start up of the LHC, it is now timely to review the state of these calculations. We review the uncertainties in estimating the black hole cross section in higher dimensions. One would like to make this estimate as precise as possible since the predicted values, or lower limits, obtain for the fundamental Planck scale and number of extra dimensions from experiments will depend directly on the accuracy of the cross section. Based on the current knowledge of the cross section, we give a range of lower limits on the fundamental Planck scale that could be obtained at LHC energies.Comment: 28 pages, 9 figures, LaTeX; added references, corrected typos, expanded discussio

Temporal and spatial dynamics of CO2 air-sea flux in the Gulf of Maine

Ocean surface layer carbon dioxide (CO2) data collected in the Gulf of Maine from 2004 to 2008 are presented. Monthly shipboard observations are combined with additional higher‐resolution CO2 observations to characterize CO2 fugacity ( fCO2) and CO2 flux over hourly to interannual time scales. Observed fCO2 andCO2 flux dynamics are dominated by a seasonal cycle, with a large spring influx of CO2 and a fall‐to‐winter efflux back to the atmosphere. The temporal results at inner, middle, and outer shelf locations are highly correlated, and observed spatial variability is generally small relative to the monthly to seasonal temporal changes. The averaged annual flux is in near balance and is a net source of carbon to the atmosphere over 5 years, with a value of +0.38 mol m−2 yr−1. However, moderate interannual variation is also observed, where years 2005 and 2007 represent cases of regional source (+0.71) and sink (−0.11) anomalies. We use moored daily CO2 measurements to quantify aliasing due to temporal undersampling, an important error budget term that is typically unresolved. The uncertainty of our derived annual flux measurement is ±0.26 mol m−2 yr−1 and is dominated by this aliasing term. Comparison of results to the neighboring Middle and South Atlantic Bight coastal shelf systems indicates that the Gulf of Maine exhibits a similar annual cycle and range of oceanic fCO2 magnitude but differs in the seasonal phase. It also differs by enhanced fCO2 controls by factors other than temperature‐driven solubility, including biological drawdown, fall‐to‐winter vertical mixing, and river runoff

Quantum corrections from a path integral over reparametrizations

We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-$N$ QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the L\"uscher term associated with $d=26$ dimensions and propose a modification of the ansatz which reproduces the L\"uscher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the L\"uscher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly

Combinatorics of Boundaries in String Theory

We investigate the possibility that stringy nonperturbative effects appear as holes in the world-sheet. We focus on the case of Dirichlet string theory, which we argue should be formulated differently than in previous work, and we find that the effects of boundaries are naturally weighted by $e^{-O(1/g_{\rm st})}$.Comment: 12 pages, 2 figures, LaTe

Growth, Condition, and Trophic Relations of Stocked Trout in Southern Appalachian Mountain Streams

Stream trout fisheries are among the most popular and valuable in the United States, but many are dependent on hatcheries to sustain fishing and harvest. Thus, understanding the ecology of hatchery‐reared trout stocked in natural environments is fundamental to management. We evaluated the growth, condition, and trophic relations of Brook Trout Salvelinus fontinalis, Brown Trout Salmo trutta, and Rainbow Trout Oncorhynchus mykiss that were stocked in southern Appalachian Mountain streams in western North Carolina. Stocked and wild (naturalized) trout were sampled over time (monthly; September 2012–June 2013) to compare condition and diet composition and to evaluate temporal dynamics of trophic position with stable isotope analysis. Relative weights (Wr) of stocked trout were inversely associated with their stream residence time but were consistently higher than those of wild trout. Weight loss of harvested stocked trout was similar among species and sizes, but fish stocked earlier lost more weight. Overall, 40% of 141 stomachs from stocked trout were empty compared to 15% of wild trout stomachs (N = 26). We identified a much higher rate of piscivory in wild trout (18 times that of stocked trout), and wild trout were 4.3 times more likely to consume gastropods relative to stocked trout. Hatchery‐reared trout were isotopically similar to co‐occurring wild fish for both δ13C and δ15N values but were less variable than wild trout. Differences in sulfur isotope ratios (δ34S) between wild and hatchery‐reared trout indicated that the diets of wild fish were enriched in δ34S relative to the diets of hatchery‐reared fish. Although hatcheryreared trout consumed prey items similar to those of wild fish, differences in consumption or behavior (e.g., reduced feeding) may have resulted in lower condition and negative growth. These findings provide critical insight on the trophic dynamics of stocked trout and may assist in developing and enhancing stream trout fisheries