Is the third coefficient of the Jones knot polynomial a quantum state of gravity?

Some time ago it was conjectured that the coefficients of an expansion of the Jones polynomial in terms of the cosmological constant could provide an infinite string of knot invariants that are solutions of the vacuum Hamiltonian constraint of quantum gravity in the loop representation. Here we discuss the status of this conjecture at third order in the cosmological constant. The calculation is performed in the extended loop representation, a generalization of the loop representation. It is shown that the the Hamiltonian does not annihilate the third coefficient of the Jones polynomal ($J_3$) for general extended loops. For ordinary loops the result acquires an interesting geometrical meaning and new possibilities appear for $J_3$ to represent a quantum state of gravity.Comment: 22 page

The Extended Loop Representation of Quantum Gravity

A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum Gravity can be realized on the state space of extended loop dependent wavefunctions. The extended representation generalizes the loop representation and contains this representation as a particular case. The resulting diffeomorphism and hamiltonian constraints take a very simple form and allow to apply functional methods and simplify the loop calculus. In particular we show that the constraints are linear in the momenta. The nondegenerate solutions known in the loop representation are also solutions of the constraints in the new representation. The practical calculation advantages allows to find a new solution to the Wheeler-DeWitt equation. Moreover, the extended representation puts in a precise framework some of the regularization problems of the loop representation. We show that the solutions are generalized knot invariants, smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1

Extended Loops: A New Arena for Nonperturbative Quantum Gravity

We propose a new representation for gauge theories and quantum gravity. It can be viewed as a generalization of the loop representation. We make use of a recently introduced extension of the group of loops into a Lie Group. This extension allows the use of functional methods to solve the constraint equations. It puts in a precise framework the regularization problems of the loop representation. It has practical advantages in the search for quantum states. We present new solutions to the Wheeler-DeWitt equation that reinforce the conjecture that the Jones Polynomial is a state of nonperturbative quantum gravity.Comment: 12pp, Revtex, no figures, CGPG-93/12-

Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure

We generalize the idea of Vassiliev invariants to the spin network context, with the aim of using these invariants as a kinematical arena for a canonical quantization of gravity. This paper presents a detailed construction of these invariants (both ambient and regular isotopic) requiring a significant elaboration based on the use of Chern-Simons perturbation theory which extends the work of Kauffman, Martin and Witten to four-valent networks. We show that this space of knot invariants has the crucial property -from the point of view of the quantization of gravity- of being loop differentiable in the sense of distributions. This allows the definition of diffeomorphism and Hamiltonian constraints. We show that the invariants are annihilated by the diffeomorphism constraint. In a companion paper we elaborate on the definition of a Hamiltonian constraint, discuss the constraint algebra, and show that the construction leads to a consistent theory of canonical quantum gravity.Comment: 21 Pages, RevTex, many figures included with psfi

Detection of serum antibodies to hepatitis E virus in domestic pigs in Italy using a recombinant swine HEV capsid protein

Background: The hepatitis E virus (HEV) has been detected in both humans and animals, particularly pigs, worldwide. Several evidences, including human infection following consumption of raw contaminated meat, suggest a zoonotic transmission of HEV. In Italy, large circulation of genotype 3 HEV has been reported in swine, and recent studies have confirmed the involvement of this genotype in autochthonous human cases. Result: In this study 111 sera collected from healthy pigs in two Italian regions were tested for anti-HEV IgG antibodies. For specific HEV antibody detection in swine, we developed ELISA and Western blotting methods, using a truncated capsid (ORF2) protein lacking the first 111 amino acids of a swine HEV genotype 3 strain. The ORF2-based ELISA revealed anti-HEV antibodies in 104 out of 111 pigs compared with 102 detected with a commercial ELISA kit. A lower number of sera reacted with the recombinant ORF2 protein in a Western blotting format (81/111). Using a Latent class analysis (LCA), the estimated sensitivities for ELISA-ORF2 and ELISA-kit tests were 0.961 and 0.936, respectively, whereas specificities were 0.599 and 0.475. The estimated sensitivity of Western blotting was 0.775, and the specificity was 0.944. Conclusions: The overall results confirm the high prevalence of HEV seropositive healthy pigs in Italy. Through comparisons with a commercial ELISA test, the swine genotype 3 HEV antigen produced in this study was proven suitable to detect anti-HEV antibodies in pig sera by both ELISA and Western Blotting

The influence of closed or open grip type during a pull-up test to exhaustion

The aim of this study is to assess whether a closed (CG) or open grip (OC) can influence the maximum number of repetitions during the pull-up test to exhaustion. Ninety-five physically active males (age 23.5 ± 6.2 years, body mass 69 ± 7.9 kg, height 174.0 ± 6.4 cm, BMI 22.9 ± 2.2) randomly performed the pull-up test to exhaustion twice, once for each type of grip, one week apart. No significant difference (p = 0.092) was found between the maximum number of repetitions performed with the OG (14.2 ± 5.7) or the CG (13.9 ± 5.9). Spearman's correlation showed no significant association between participants' body mass and the number of repetitions (r = 0.128, p = 0.22 for OG; r = 0.157, p = 0.13 for CG). According to our results, the grip is not relevant in the determination of the performance during a pull-up test to exhaustion. Thus, using one grip instead of another may be recommended independently of performance needs. Grip type may be adapted considering the practised sport, and specific athletic requirements, as well as individual preference

Correlation between micro and macrostructural biaxial behavior of ascending thoracic aneurysm: a novel experimental technique

Mechanical properties and microstructural modifications of vessel tissues are strongly linked, as established in the state of the art of cardiovascular diseases. Techniques to obtain both mechanical and structural information are reported, but the possibility to obtain real-time microstructural and macrostructural data correlated is still lacking. An experimental approach to characterize the aortic tissue is presented. A setup integrating biaxial traction and Small Angle Light Scattering (SALS) analysis is described. The system was adopted to test ex-vivo aorta specimens from healthy and aneusymatic (aTAA) cases. A significant variation of the fiber dispersion with respect to the unloaded state was encountered during the material traction. The corresponding microstructural and mechanical data were successfully used to fit a given anisotropic constitutive model, with satisfactory R2 values (0.97±0.11 and 0.96±0.17, for aTAA and healthy population, respectively) and fiber dispersion parameters variations between the aTAA and healthy populations (0.39±0.23 and 0.15±0.10). The method integrating the biaxial/SALS technique was validated, allowing for real-time synchronization between mechanical and microstructural analysis of anisotropic biological tissues

Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants

We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wavefunctions based on the Vassiliev knot invariants. The constraints are finite, well defined, and reproduce at the level of quantum commutators the Poisson algebra of constraints of the classical theory. A similar construction can be carried out in 2+1 dimensions leading to the correct quantum theory.Comment: 4 pages, RevTex, one figur

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0