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.
118438482
Quantum Matrix Pairs
The notion of quantum matrix pairs is defined. These are pairs of matrices with noncommuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of powers of the matrices obey the same pattern of internal relations as the original pair. Such matrices appear in an approach by the authors to quantizing gravity in 2 space and 1 time dimensions with negative cosmological constant on the torus. Explicit examples and transformations which generate new pairs from a given pair are presented.
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.
118244731
Covariant canonical formalism for gravity and supergravity.
121859529
Extended canonical vierbein formalism
Abstract The canonical vierbein theory, written in the language of differential forms, is extended to include the differentials themselves as independent fields. The resulting theory strongly resembles the BRST extension of the component theory provided the hamiltonian is identified with the BRST charge Q and the differentials dx i with the spatial projections of the ghosts.
115616794
Charmless semileptonic decays of B mesons
The authors have used the CLEO II detector at the CESR storage ring to study the endpoint region of the B-meson semileptonic momentum spectrum. Lepton production above the kinematic limit for b{r_arrow}cl{nu} is confirmed, although at a level which is smaller than has been observed previously. Model-dependent estimates os the ratio {vert_bar}V{sub ub}{vert_bar}/{vert_bar}V{sub cb}{vert_bar} will be reported.
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.