Artificial Intelligence, Expert Systems and Law

Artificial Intelligence, Expert Systems and La

Correspondence between Minkowski and de Sitter Quantum Field Theory

In this letter we show that the ``preferred'' Klein-Gordon Quantum Field Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral condition can be obtained as superposition of d-dimensional de Sitter Klein-Gordon fields in the preferred vacuum. These results establish a correspondence between QFT's living on manifolds having different dimensions. The method exposed here can be applied to study other situations and notably QFT on Anti de Sitter spacetime.Comment: 7 pages, no figures, typos corrected, added one referenc

Validation of AIRS V6 Surface Temperature over Greenland with GCN and NOAA Stations

This work compares the temporal and spatial characteristics of the AIRSAMSU (Atmospheric Infrared Sounder Advanced Microwave Sounding Unit A) Version 6 and MODIS (Moderate resolution Imaging Spectroradiometer) Collection 5 derived surface temperatures over Greenland. To estimate uncertainties in space-based surface temperature measurements, we re-projected the MODIS Ice Surface Temperature (IST) to 0.5 by 0.5 degree spatial resolution. We also re-gridded AIRS Skin Temperature (Ts) into the same grid but classified with different cloud conditions and surface types. These co-located data sets make intercomparison between the two instruments relatively straightforward. Using this approach, the spatial comparison between the monthly mean AIRS Ts and MODIS IST is in good agreement with RMS 2K for May 2012. This approach also allows the detection of any long-term calibration drift and the careful examination of calibration consistency in the MODIS and AIRS temperature data record. The temporal correlations between temperature data are also compared with those from in-situ measurements from GC-Net (GCN) and NOAA stations. The coherent time series of surface temperature evident in the correlation between AIRS Ts and GCN temperatures suggest that at monthly time scales both observations capture the same climate signal over Greenland. It is also suggested that AIRS surface air temperature (Ta) can be used to estimate the boundary layer inversion

SU(2) Flux Distributions on Finite Lattices

We studied SU(2) flux distributions on four dimensional euclidean lattices with one dimension very large. By choosing the time direction appropriately we can study physics in two cases: one is finite volume in the zero temperature limit, another is finite temperature in the the intermediate to large volume limit. We found that for cases of beta > beta crit there is no intrinsic string formation. Our lattices with beta > beta crit belong to intermediate volume region, and the string tension in this region is due to finite volume effects. In large volumes we found evidence for intrinsic string formation.Comment: 21 pages text, 12 pages of postscript figure

Duality in Scalar Field Theory on Noncommutative Phase Spaces

We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to interactions defined with a star-product, of that which arises in quantum field theories of non-interacting scalar particles coupled to a constant background electromagnetic field. The dual models are in general of the same original form but with transformed coupling parameters, while in certain special cases all parameters are essentially unchanged. Using a particular regualarization we show, to all orders of perturbation theory, that that this duality also persists at the quantum level. We also point out various other properties of this class of noncommutative field theories.Comment: 13 pages LaTeX; Minor corrections, references added, comment about self-dual models added to section

Brane World Gravity in an AdS Black Hole

We consider a model of brane world gravity in the context of non-conformal non-SUSY matter. In particular we modify the earlier strong coupling solution to the glueball spectrum in an $AdS^7$ Black Hole by introducing a Randall-Sundrum Planck brane as a UV cut-off. The consequence is a new normalizable zero mass tensor state, which gives rise to an effective Einstein-Hilbert theory of gravity, with exponentially small corrections set by the mass gap to the discrete glueball spectrum. However the simplest microscopic theory for the Planck brane is found to have a tachyonic instability in the radion mode.Comment: 25 pages, late

String windings in the early universe

We study string dynamics in the early universe. Our motivation is the proposal of Brandenberger and Vafa, that string winding modes may play a key role in decompactifying three spatial dimensions. We model the universe as a homogeneous but anisotropic 9-torus filled with a gas of excited strings. We adopt initial conditions which fix the dilaton and the volume of the torus, but otherwise assume all states are equally likely. We study the evolution of the system both analytically and numerically to determine the late-time behavior. We find that, although dynamical evolution can indeed lead to three large spatial dimensions, such an outcome is not statistically favored.Comment: 26 pages, LaTeX, 4 eps figure

Hamiltonian domain wall fermions at strong coupling

We apply strong-coupling perturbation theory to gauge theories containing domain-wall fermions in Shamir's surface version. We construct the effective Hamiltonian for the color-singlet degrees of freedom that constitute the low-lying spectrum at strong coupling. We show that the effective theory is identical to that derived from naive, doubled fermions with a mass term, and hence that domain-wall fermions at strong coupling suffer both doubling and explicit breaking of chiral symmetry. Since we employ a continuous fifth dimension whose extent tends to infinity, our result applies to overlap fermions as well.Comment: Revtex, 21 pp. Some changes in Introduction, dealing with consistency with previous wor

Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions

The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only topological numbers of Heisenberg modules and enables extraction of the weak-coupling limit of the gauge theory. A dual algebraic expansion involves only group theoretic quantities, winding numbers and translational zero modes, and enables analysis of the strong-coupling limit of the gauge theory and the high-momentum behaviour of open Wilson lines. The dual expressions can be interpreted physically as exact sums over contributions from virtual electric dipole quanta.Comment: 37 pages. References adde

Cosmology From Random Multifield Potentials

We consider the statistical properties of vacua and inflationary trajectories associated with a random multifield potential. Our underlying motivation is the string landscape, but our calculations apply to general potentials. Using random matrix theory, we analyze the Hessian matrices associated with the extrema of this potential. These potentials generically have a vast number of extrema. If the cross-couplings (off-diagonal terms) are of the same order as the self-couplings (diagonal terms) we show that essentially all extrema are saddles, and the number of minima is effectively zero. Avoiding this requires the same separation of scales needed to ensure that Newton's constant is stable against radiative corrections in a string landscape. Using the central limit theorem we find that even if the number of extrema is enormous, the typical distance between extrema is still substantial -- with challenging implications for inflationary models that depend on the existence of a complicated path inside the landscape.Comment: revtex, 3 figures, 10 pages v2 refs adde