Embedded graph invariants in Chern-Simons theory

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines - an embedded graph invariant. Using a slight generalization of the variational method, lowest-order results for invariants for arbitrary valence graphs are derived; gauge invariant operators are introduced; and some higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. Though, without a global projection of the graph, there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity - as a way of relating frames at distinct vertices.Comment: 20 pages; RevTex; with approx 50 ps figures; References added, introduction rewritten, version to be published in Nuc. Phys.

High-Efficiency Resonant RF Spin Rotator with Broad Phase Space Acceptance for Pulsed Polarized Cold Neutron Beams

We have developed a radio-frequency resonant spin rotator to reverse the neutron polarization in a 9.5 cm x 9.5 cm pulsed cold neutron beam with high efficiency over a broad cold neutron energy range. The effect of the spin reversal by the rotator on the neutron beam phase space is compared qualitatively to RF neutron spin flippers based on adiabatic fast passage. The spin rotator does not change the kinetic energy of the neutrons and leaves the neutron beam phase space unchanged to high precision. We discuss the design of the spin rotator and describe two types of transmission-based neutron spin-flip efficiency measurements where the neutron beam was both polarized and analyzed by optically-polarized 3He neutron spin filters. The efficiency of the spin rotator was measured to be 98.0+/-0.8% on resonance for neutron energies from 3.3 to 18.4 meV over the full phase space of the beam. As an example of the application of this device to an experiment we describe the integration of the RF spin rotator into an apparatus to search for the small parity-violating asymmetry A_gamma in polarized cold neutron capture on para-hydrogen by the NPDGamma collaboration at LANSCE

Growth and Regional Inequality in China During the Reform Era

Chinese city-level data indicate that differences in growth rates are far more severe than indicated in previous studies which typically use data at higher levels of aggregation. We estimate growth equations using city-level data and find that the policy of awarding a special economic zone status enhances growth substantially, increasing annual growth rates by 5.5 percentage points. Annual growth rates of open coastal cities are, on average, 3 percentage points higher. Our qualitative results on the role of policy and the effects of FDI are similar to those of earlier studies that have employed provincial-level data; but, quantitatively, our results are substantially different. We also provide evidence of an indirect role of policy in the growth process through its ability to attract growth-enhancing foreign direct investment.http://deepblue.lib.umich.edu/bitstream/2027.42/39946/2/wp561.pd

Critical Pebbling Numbers of Graphs

We define three new pebbling parameters of a connected graph $G$, the $r$-, $g$-, and $u$-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices $n$ and the diameter $d$ of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the $r$-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the $r$-critical pebbling number is $2^d$.Comment: 26 page

Recursive strategy for decomposing Betti tables of complete intersections

We introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition. We also provide a detailed analysis of the Boij-Soederberg decomposition for Betti diagrams of codimension four complete intersections where the largest generating degree satisfies the size condition

On the Universality of the Entropy-Area Relation

We present an argument that, for a large class of possible dynamics, a canonical quantization of gravity will satisfy the Bekenstein-Hawking entropy-area relation. This result holds for temperatures low compared to the Planck temperature and for boundaries with areas large compared to Planck area. We also relate our description, in terms of a grand canonical ensemble, to previous geometric entropy calculations using area ensembles.Comment: 6 page

Cosmological Histories for the New Variables

Histories and measures for quantum cosmology are investigated through a quantization of the Bianchi IX cosmology using path integral techniques. The result, derived in the context of Ashtekar variables, is compared with earlier work. A non-trivial correction to the measure is found, which may dominate the classical potential for universes on the Planck scale.Comment: 14, CGPG-94/2-

On plane gravitational waves in real connection variables

We investigate using plane fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis, we start with planar symmetric space-times in the real connection formulation. We reduce via Dirac constraint analysis to a final form with one canonical pair and one constraint, equivalent to the metric and Einstein equations of plane-fronted with parallel rays waves. Due to the symmetries and use of special coordinates general covariance is broken. However, this allows us to simply express the constraints of the consistent system. A recursive construction of Dirac brackets results in non-local brackets, analogous to those of self-dual fields, for the triad variables chosen in this approach.Comment: v2: Matches published version, up to minor stylistic change

On the q-quantum gravity loop algebra

A class of deformations of the q-quantum gravity loop algebra is shown to be incompatible with the combinatorics of Temperley-Lieb recoupling theory with deformation parameter at a root of unity. This incompatibility appears to extend to more general deformation parameters.Comment: v2: text clarified, version to be publishe

Towards Loop Quantization of Plane Gravitational Waves

The polarized Gowdy model in terms of Ashtekar-Barbero variables is further reduced by including the Killing equations for plane-fronted parallel gravitational waves with parallel rays. The resulting constraint algebra, including one constraint derived from the Killing equations in addition to the standard ones of General Relativity, are shown to form a set of first-class constraints. Using earlier work by Banerjee and Date the constraints are expressed in terms of classical quantities that have an operator equivalent in Loop Quantum Gravity, making space-times with pp-waves accessible to loop quantization techniques.Comment: 14 page