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.
119542912
The canonical Hamiltonian for vierbein general relativity
The canonical Hamiltonian for vierbein general relativity is derived, starting from an expression for the action which differs from the Hilbert-Einstein action by a surface term. Results are given both in the proper time formalism and in time gauge.
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.
118956967
Constants of the Motion and the Quantum Modular Group in (2+1) - Dimensional Gravity
Constants of motion are calculated for 2+1 dimensional gravity with topology R \times T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters, and the modular group is generated by these conserved quantities. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to the conformal algebra so(2,3).
119143192
Quantum Holonomies in (2+1)-Dimensional Gravity
We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and upper-triangular form are constructed, which in the latter case exhibit additional, non-trivial internal relations for each holonomy matrix. Representations are constructed and a group of transformations - a quasi-modular group - which preserves this structure, is presented.
44620547
Quantization of 2+1 gravity for genus 2.
In [1,2] we established and discussed the algebra of observables for $2+1$ gravity at both the classical and quantum level, and gave a systematic discussion of the reduction of the expected number of independent observables to $6g - 6 (g > 1)$. In this paper the algebra of observables for the case $g=2$ is reduced to a very simple form. A Hilbert space of state vectors is defined and its representations are discussed using a deformation of the Euler-Gamma function. The deformation parameter $\th$ depends on the cosmological and Planck's constants.
16014194
The interaction of a giant planet with a disc with MHD turbulence - I. The initial turbulent disc models
This is the first of a series of papers aimed at developing and interpreting simulations of protoplanets interacting with turbulent accretion discs. In this first paper we study the turbulent disc models prior to the introduction of a perturbing protoplanet. We study cylindrical disc models in which a central domain is in Keplerian rotation and unstable to the magnetorotational instability. Models of varying disc size and aspect ratio H/r are considered with magnetic fields having zero net flux. We relate the properties of the turbulent models to classical viscous disc theory. All models were found to attain a turbulent state in their Keplerian domains with volume averaged stress parameter α ∼ 5 × 10 −3 . At any particular time the vertically and azimuthally averaged value exhibited large fluctuations in radius. However, an additional time average over periods exceeding three orbital periods at the outer boundary of the Keplerian domain resulted in a more smoothly varying quantity with radial variations within a factor of 2 or so. The vertically and azimuthally averaged radial velocity showed much larger spatial and temporal fluctuations, requiring additional time averaging for at least seven to eight orbital periods at the outer boundary of the Keplerian domain to limit them. Comparison with the value derived from the averaged stress using viscous disc theory yielded schematic agreement for feasible averaging times but with some indication that the effects of residual fluctuations remained. The behaviour described above must be borne in mind when considering laminar disc simulations with anomalous Navier‐Stokes viscosity. This is because the operation of a viscosity, as in classical viscous disc theory with anomalous viscosity coefficient, cannot apply to a turbulent disc undergoing rapid changes due to external perturbation. The classical theory can only be used to describe the time averaged behaviour of the parts of the disc that are in a statistically steady condition long enough for appropriate averaging to be carried out.
108864186
MINOS near-detector coil design
The 980-ton MINOS near detector will be installed in the new NuMI near hall at 100m below grade at Fermilab. It will be assembled from 282 1-inch thick steel plates. The planes are made from low carbon (1006), hot rolled steel and are toroidally magnetized. Each plane will be hung by two 'ears', which are extensions of the octagonal plane structure, similar to the hanging files in a file drawer. The plates have a center-to-center spacing of 5.94 cm. This document has been prepared for the 8/99 Conceptual Design Review of the MINOS near detector coil. It's main goal is to provide a set of references to previous documents and to assemble various design drawings and engineering calculations that have not been included in previous technical memos. It also provides some background material relevant for the coil implementation. Much of the text for this document is edited from the MINOS Detectors Technical Design Report.