Loop Representations for 2+1 Gravity on a Torus

We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this system. In particular, we look at the loop transform in the part of the phase space where the holonomies are boosts and study its kernel. This kernel is dense in the connection representation and the transform is not continuous with respect to the natural topologies, even in its domain of definition. Nonetheless, loop representations isomorphic to the connection representation corresponding to this part of the phase space can still be constructed if due care is taken. We present this construction but note that certain ambiguities remain; in particular, functions of loops cannot be uniquely associated with functions of connections.Comment: 24 journal or 52 preprint pages, revtex, SU-GP-93/3-

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-

Dirac-like approach for consistent discretizations of classical constrained theories

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the Poisson or Dirac bracket structure. The conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated Lagrange multipliers. The gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations. The resulting scheme is general enough to accommodate the treatment of field theories on the lattice. This paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems, including Yang--Mills theories, BF-theory and general relativity on the lattice.Comment: 11 pages, RevTe

Classical Loop Actions of Gauge Theories

Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.Comment: LaTeX 14 page

A finite spin-foam-based theory of three and four dimensional quantum gravity

Starting from Ooguri's construction for $BF$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the evolution operators of the theory are exact solutions of the Hamiltonian constraint of quantum gravity proposed by Thiemann. The resulting theory is the first example of a well defined, finite, consistent, spin-foam based theory in a situation with an infinite number of degrees of freedom. Since it solves the quantum constraints of general relativity it is also a candidate for a theory of quantum gravity. It is likely, however, that the solutions constructed correspond to a spurious sector of solutions of the constraints. The richness of the resulting theory makes it an interesting example to be analyzed by forthcoming techniques that construct the semi-classical limit of spin network quantum gravity

A Discrete Time Presentation of Quantum Dynamics

Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any approximation or explicit discretization, mimics features of the discrete time evolution of loop quantum cosmology. We discuss the continuum limit, physical inner product and matrix elements of physical observables to bring out various issues regarding viability of a discrete evolution. We also point out how a continuous time could emerge without appealing to any continuum limit.Comment: 20 pages, RevTex, no figures. Additional Clarifications added. Version accepted for publication in Class. Quant. Gra

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

Prevalence of hepatitis E virus in Italian pig herds. Preliminary results

Hepatitis E virus (HEV) is the causative agent of hepatitis E, and is an unenveloped positive sense single-stranded RNA wus. Swine HEV strains are genetically closely related to human strains from the same area, suggesting the occurrence of zoonotic transmission. Recently, human cases of hepatitis E have been linked to the consumption of raw or undercooked meat or organs from deer, wild boars or p1gs. The disease is now considered an emerging food-borne transmitted zoonosis. During 2006, a pilot investigation was performed to determine the prevalence of HEV in pig farms located in Northern Italy. 274 faecal samples were collected from healthy fattening animals (3-4 and 8-9 months of age) and from healthy breeding animals (gilts and sows) from 6 different farms, and analyzed using a Nested-RT-PCR targeting the open reading frame 2 (ORF2) region. Stool samples were suspended in water, and viral RNA extraction was performed using a commercial kit. Extracted viral RNA was subjected to RT-PCR amplification using degenerate primers conA 1-conS1 for the first amplification, and degenerate primers conA2-conS2 for the nested PCR, yielding a final fragment of 145 bp. HEV RNA was detected in sixty-nine of the 274 (25.2%) examined samples. None of the six farms resulted negative and the prevalence within the farms ranged between 2% and 60.5% For the characterization of the strains, randomly selected positive samples were subjected to nucleotide sequencing, and aligned with those present in the NCBI Data Bank Sequence analysis showed that all stra1ns were Swine Hepatitis E belonging to Genotype 3. These preliminary results confirm that swine HEV is widespread in Italian swine farms