Involution and Constrained Dynamics I: The Dirac Approach

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an involutive system. We discuss the implications of this identification for field theories and argue that the involution analysis is more general and flexible than the Dirac approach. We also derive intrinsic expressions for the number of degrees of freedom.Comment: 28 pages, latex, no figure

On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

A Factorization Algorithm for G-Algebras and Applications

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \in \mathcal{G}$, where $\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field. Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\"obner basis algorithm for $G$-algebras. This algorithm is useful for various applications, e.g. in analysis of solution spaces of systems of linear partial functional equations with polynomial coefficients, coming from $\mathcal{G}$. Additionally, it is possible to include inequality constraints for ideals in the input

Discrete Symmetry Enhancement in Nonabelian Models and the Existence of Asymptotic Freedom

We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by L"uscher, Weisz and Wolff [1] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.Comment: 18 pages, 8 figures Color coding in Fig. 5 changed to improve visibilit

Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.Comment: To appear in Phys. Rev. Lett. Significant new results. One figure removed due to page limitatio

Risk for Clostridium difficile infection after allogeneic hematopoietic cell transplant remains elevated in the postengraftment period

BACKGROUND: Clostridium difficile infection (CDI) is a frequent cause of diarrhea among allogeneic hematopoietic cell transplant (HCT) recipients. It is unknown whether risk factors for CDI vary by time posttransplant. METHODS: We performed a 3-year prospective cohort study of CDI in allogeneic HCT recipients. Participants were enrolled during their transplant hospitalizations. Clinical assessments were performed weekly during hospitalizations and for 12 weeks posttransplant, and monthly for 30 months thereafter. Data were collected through patient interviews and chart review, and included CDI diagnosis, demographics, transplant characteristics, medications, infections, and outcomes. CDI cases were included if they occurred within 1 year of HCT and were stratified by time from transplant. Multivariable logistic regression was used to determine risk factors for CDI. RESULTS: One hundred eighty-seven allogeneic HCT recipients were enrolled, including 63 (34%) patients who developed CDI. 38 (60%) CDI cases occurred during the preengraftment period (days 0-30 post-HCT) and 25 (40%) postengraftment (day >30). Lack of any preexisting comorbid disease was significantly associated with lower risk of CDI preengraftment (odds ratio [OR], 0.3; 95% confidence interval [CI], 0.1-0.9). Relapsed underlying disease (OR, 6.7; 95% CI, 1.3-33.1), receipt of any high-risk antimicrobials (OR, 11.8; 95% CI, 2.9-47.8), and graft-versus-host disease (OR, 7.8; 95% CI, 2.0-30.2) were significant independent risk factors for CDI postengraftment. CONCLUSIONS: A large portion of CDI cases occurred during the postengraftment period in allogeneic HCT recipients, suggesting that surveillance for CDI should continue beyond the transplant hospitalization and preengraftment period. Patients with continued high underlying severity of illness were at increased risk of CDI postengraftment

Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump

It is numerically shown that the discontinuous character of the helicity modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT) transition can be directly related to a higher order derivative of the free energy without presuming any {\it a priori} knowledge of the nature of the transition. It is also suggested that this higher order derivative is of intrinsic interest in that it gives an additional characteristics of the KT transition which might be associated with a universal number akin to the universal value of the helicity modulus at the critical temperature.Comment: 4 pages, to appear in PR