123450790
THE MAPPING CLASS GROUP FOR GENUS 2
This article represents joint work with Tullio Regge and essentially concerns the symmetries of the hexagon. When space {Sigma} is a genus 2 Riemann surface the observable of the theory are the gauge-invariant normalized traces of the SL(2,R) matrices which form the spinor representation of {pi}{sub 1}({Sigma}). It was extremely difficult to find a suitable notation for the 15 possible traces, in fact we shall simultaneously use two equivalent (and hopefully not too ambiguous) notations which are now described. First, define B{sub n} = c(U{sub 1}{sup a}V{sub 1}{sup b}U{sub 2}{sup c}V{sub 2}{sup d}) where c(x) = 1/2 Tr(x), x element of {pi}{sub 1}, and n = a + 2b +4c + 8d = 1 . . . 15. There are two exception to , namely B{sub 3} = c (U{sub 1}V{sub 1}{sup {minus}1}) and B{sub 12} = c(U{sub 2}V{sub 2}{sup {minus}1}). SL(2,R) identities will reduce all other traces. These can be arranged to fit on a hexagon where each line, internal or on the border, represents one of the B{sub n}. Instead of numbering the lines number the points so that, for example, B{sub 1} is equivalent to A{sub 12}, B{sub 5} to A{sub 36}, with A{sub ij} = A{submore » ji}, where we use different letters A,B, to avoid confusion. This is the second notation. They can be related through the 6 {times} 6 symmetric matrix A{sub ij} whose components are precisely the elements A{sub ij} and A{sub ii} (no sum) = 1.« less
120048132
Canonical normal coordinates
We examine the advantages and disadvantages of fixing the coordinate gauge to be that of the Riemann normal coordinates by applying the Dirac formalism for constrained canonical systems in general relativity.
117052872
Normal coordinates in canonical form
126036591
Lorentz invariance and the group manifold approach
124467838
Lorentz Invariance in tangent space
5325226
A QUANTUM GOLDMAN BRACKET FOR LOOPS ON SURFACES
In the context of (2+1)–dimensional gravity, we use holonomies of constant connections which generate a q–deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops. We use these features to determine a quantum Goldman bracket (commutator) for intersecting loops on surfaces, and discuss the resulting quantum geometry.
120224392
The effects of neutron irradiation on multi-pixel hybrid photodiode tubes
Abstract The effects of neutron irradiation on a multi-pixel hybrid photodiode tube (HPD) were studied. The HPD underwent an integrated fluence of 10 13 neutrons cm 2 from a 252 Cf source. Increased leakage currents were observed during this irradiation, consistent with that observed from bare silicon detectors. The HPD was observed to be fully operational, with acceptable leakage currents, at the fluences expected during the lifetime of the CMS experiment. After the full dosage, small intrapixel inhomogeneities were observed in the HPD's response. The origins of these inhomogeneities and methods to mitigate the radiation damage were investigated.
122041574
Multi-pixel hybrid photodiode tubes for the CMS hadron calorimeter
Abstract Avalanche Photodiodes and 7-channel HPDs from DEP were installed on a prototype CMS HCAL and their response to muons, electrons and pions was measured in a test beam. DC response to a radioactive source used to calibrate the tiles was also studied. Increase in leakage current in the HPD from an integrated dose of 10 13 neutrons/cm 2 was observed using a Cf source.