Noncommutative Quantum Gravity

The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a complex Hermitian, nonsymmetric $g_{\mu\nu}$ and discuss the problems associated with such a theory. We then introduce a complex symmetric (non-Hermitian) metric, with the associated complex connection and curvature, as the basis of a noncommutative spacetime geometry. The spacetime coordinates are in general complex and the group of local gauge transformations is associated with the complex group of Lorentz transformations CSO(3,1). A real action is chosen to obtain a consistent set of field equations. A Weyl quantization of the metric associated with the algebra of noncommuting coordinates is employed.Comment: 13 pages LaTex. Changes to text and new text added. To be published in Physics Letters

ELM triggering conditions for the integrated modeling of H-mode plasmas

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. Formation of the pedestal and the L-H transition is the direct result of ExB flow shear suppression of anomalous transport. The periodic ELM crashes are triggered by either the ballooning or peeling MHD instabilities. The BALOO, DCON, and ELITE ideal MHD stability codes are used to derive a new parametric expression for the peeling-ballooning threshold. The new dependence for the peeling-ballooning threshold is implemented in the ASTRA transport code. Results of integrated modeling of DIII-D like discharges are presented and compared with experimental observations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete

Noncommutative Topological Theories of Gravity

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies.Comment: 17+1 pages, LaTeX, no figures, some clarifications, comments and references added, style improve

Exploring morphological correlations among H2CO, 12CO, MSX and continuum mappings

There are relatively few H2CO mappings of large-area giant molecular cloud (GMCs). H2CO absorption lines are good tracers for low-temperature molecular clouds towards star formation regions. Thus, the aim of the study was to identify H2CO distributions in ambient molecular clouds. We investigated morphologic relations among 6-cm continuum brightness temperature (CBT) data and H2CO (111-110; Nanshan 25-m radio telescope), 12CO (1--0; 1.2-m CfA telescope) and midcourse space experiment (MSX) data, and considered the impact of background components on foreground clouds. We report simultaneous 6-cm H2CO absorption lines and H110\alpha radio recombination line observations and give several large-area mappings at 4.8 GHz toward W49 (50'\times50'), W3 (70'\times90'), DR21/W75 (60'\times90') and NGC2024/NGC2023 (50'\times100') GMCs. By superimposing H2CO and 12CO contours onto the MSX color map, we can compare correlations. The resolution for H2CO, 12CO and MSX data was about 10', 8' and 18.3", respectively. Comparison of H2CO and 12CO contours, 8.28-\mu m MSX colorscale and CBT data revealed great morphological correlation in the large area, although there are some discrepancies between 12CO and H2CO peaks in small areas. The NGC2024/NGC2023 GMC is a large area of HII regions with a high CBT, but a H2CO cloud to the north is possible against the cosmic microwave background. A statistical diagram shows that 85.21% of H2CO absorption lines are distributed in the intensity range from -1.0 to 0 Jy and the \Delta V range from 1.206 to 5 km/s.Comment: 18 pages, 22 figures, 5 tables. Accepted to be published in Astrophysics and Space Scienc