Completeness of Wilson loop functionals on the moduli space of SL(2,C)SL(2,C) and SU(1,1)SU(1,1)-connections

The structure of the moduli spaces \M := \A/\G of (all, not just flat) $SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any topology on the corresponding spaces \A of all connections which satisfies the weak requirement of compatibility with the affine structure of \A, the moduli space \M is shown to be non-Hausdorff. It is then shown that the Wilson loop functionals --i.e., the traces of holonomies of connections around closed loops-- are complete in the sense that they suffice to separate all separable points of \M. The methods are general enough to allow the underlying n-manifold to be topologically non-trivial and for connections to be defined on non-trivial bundles. The results have implications for canonical quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-

Geometry of Generic Isolated Horizons

Geometrical structures intrinsic to non-expanding, weakly isolated and isolated horizons are analyzed and compared with structures which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address in detail the issue of singling out the preferred normals to these horizons required in various applications. This work provides powerful tools to extract invariant, physical information from numerical simulations of the near horizon, strong field geometry. While it complements the previous analysis of laws governing the mechanics of weakly isolated horizons, prior knowledge of those results is not assumed.Comment: 37 pages, REVTeX; Subsections V.B and V.C moved to a new Appenedix to improve the flow of main argument

Normal-superfluid interaction dynamics in a spinor Bose gas

Coherent behavior of spinor Bose-Einstein condensates is studied in the presence of a significant uncondensed (normal) component. Normal-superfluid exchange scattering leads to a near-perfect local alignment between the spin fields of the two components. Through this spin locking, spin-domain formation in the condensate is vastly accelerated as the spin populations in the condensate are entrained by large-amplitude spin waves in the normal component. We present data evincing the normal-superfluid spin dynamics in this regime of complicated interdependent behavior.Comment: 5 pages, 4 fig

Cold Molecule Spectroscopy for Constraining the Evolution of the Fine Structure Constant

We report precise measurements of ground-state, $\lambda$-doublet microwave transitions in the hydroxyl radical molecule (OH). Utilizing slow, cold molecules produced by a Stark decelerator we have improved over the precision of the previous best measurement by twenty-five-fold for the F' = 2 $\to$ F = 2 transition, yielding (1 667 358 996 $\pm$ 4) Hz, and by ten-fold for the F' = 1 $\to$ F = 1 transition, yielding (1 665 401 803 $\pm$ 12) Hz. Comparing these laboratory frequencies to those from OH megamasers in interstellar space will allow a sensitivity of 1 ppm for $\Delta\alpha/\alpha$ over $\sim$$10^{10}$ years.Comment: This version corrects minor typos in the Zeeman shift discussio

Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann's version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and links. We exhibit the matrix elements of the hamiltonian constraint operator in the spin network basis in compact algebraic form.Comment: 32 pages, 22 eps figures. LaTeX (Using epsfig.sty,ioplppt.sty and bezier.sty). Submited to Classical and Quantum Gravit

SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter

An so(4,C)-covariant hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop gravity. Dirac quantization of this system is constructed. Next we study dependence of the quantum system on the Immirzi parameter. The path integral quantization shows no dependence on it. A way to modify the loop approach in the accordance with the formalism developed here is briefly outlined.Comment: 14 pages, LATEX; minor changes; misprints corrected; commutator of two secondary second class constraints correcte

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

On the diffeomorphism commutators of lattice quantum gravity

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a variety of different discretizations of the continuum constraints, and thus generalizes an earlier calculation by Renteln.Comment: 16 pages, Te