Timeless path integral for relativistic quantum mechanics

Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\hbar$. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space. Meanwhile, the difference between relativistic quantum mechanics and conventional nonrelativistic (with time) quantum mechanics is elaborated on in light of timeless path integral.Comment: 41 pages; more references and comments added; version to appear in CQ

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated

Mixmaster Behavior in Inhomogeneous Cosmological Spacetimes

Numerical investigation of a class of inhomogeneous cosmological spacetimes shows evidence that at a generic point in space the evolution toward the initial singularity is asymptotically that of a spatially homogeneous spacetime with Mixmaster behavior. This supports a long-standing conjecture due to Belinskii et al. on the nature of the generic singularity in Einstein's equations.Comment: 4 pages plus 4 figures. A sentence has been deleted. Accepted for publication in PR

A New Limit on the Antiproton Lifetime

Measurements of the cosmic ray pbar/p ratio are compared to predictions from an inhomogeneous disk-diffusion model of pbar production and propagation within the Galaxy, combined with a calculation of the modulation of the interstellar cosmic ray spectra as the particles propagate through the heliosphere to the Earth. The predictions agree with the observed pbar/p spectrum. Adding a finite pbar lifetime to the model, we obtain the limit tau_pbar > 0.8 Myr (90 % C.L.).Comment: 13 pages, 3 encapsulated Postscript figures, uses AASTeX; accepted by Astrophysical Journal; minor change

On multi-graviton and multi-gravitino gauge theories

This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime dimensions. General possibilities for multiplication rules and coupling constants are simultaneously accommodated by regarding the set of fields equivalently as a single algebra-valued spin-2 field and single algebra-valued spin-3/2 field, where the underlying algebra is factorized into a field-coupling part and an internal multiplication part. The condition that there exist a gauge invariant Lagrangian (to within a divergence) for these algebra-valued fields is used to derive determining equations whose solutions give all allowed deformation terms, yielding nonlinear field equations and nonabelian gauge symmetries, together with all allowed formal multiplication rules as needed in the Lagrangian for demonstration of invariance under the gauge symmetries and for derivation of the field equations. In the case of spin-2 fields alone, the main result of this analysis is that all deformations (without any higher derivatives than appear in the linear theory) are equivalent to an algebra-valued Einstein gravity theory. By a systematic examination of factorizations of the algebra, a novel type of nonlinear gauge theory of two or more spin-2 fields is found, where the coupling for the fields is based on structure constants of an anticommutative, anti-associative algebra, and with formal multiplication rules that make the fields anticommuting (while products obey anti-associativity). Supersymmetric extensions of these results are obtained in the more general case when spin-3/2 fields are included.Comment: 33 pages (latex

Anti-factor Xa antibodies in patients with antiphospholipid syndrome and their effects upon coagulation assays

- Introduction: The aim of this study was to examine the prevalence and functional effects of antibodies directed against Factor (F)Xa and other serine proteases (SP) in patients with antiphospholipid syndrome (APS). - Methods: Serum from patients with APS (n = 59), systemic lupus erythematosus (SLE; n = 106), other autoimmune rheumatic disease (ARD; n = 63) and 40 healthy controls (HC) were tested for IgG activity against thrombin (Thr), FXa, FVIIa, phosphatidylserine (PS)/FXa and antithrombin (AT)-III by enzyme-linked immunosorbent assay (ELISA). Anti-FXa positive IgG were purified to measure their avidity by chaotropic ELISA and functional effects upon clotting time (FXa-ACT) and FXa enzymatic activity (± AT-III). - Results: Anti-FXa IgG were found in patients with SLE (49.1%) and APS (33.9%) (P <0.05) but not in ARD controls and HC. In contrast, anti-Thr and anti-PS/FXa IgG were identified in other ARD and anti-FVIIa IgG were low in all groups. The avidity of APS-IgG to FXa was significantly higher than SLE-IgG (P <0.05). Greatest prolongation of FXa-ACT was observed with APS-IgG and greatest inhibitory effect upon FXa enzymatic activity was found with APS-IgG followed by SLE-IgG compared to HC-IgG. ATIII inhibition of FXa was significantly reduced by APS-IgG compared with HC and SLE (P <0.05) and did not correlate with binding to AT-III. - Conclusion: APS anti-FXa IgG have higher avidity to FXa and greater effects upon the enzymatic and coagulant activity of FXa compared with SLE anti-FXa IgG. Further studies of anti-FXa antibodies in APS, SLE and other non-autoimmune thrombotic disease cohorts are now required to evaluate whether targeting FXa with selective inhibitors in patients bearing anti-FXa antibodies may be an effective treatment strategy

A manifesto for researching entrepreneurial ecosystems

Entrepreneurial ecosystems are the focus of government economic policies around the world for their potential to generate entrepreneur-led economic development. The paper identifies key research questions and challenges to building effective public policy: (i) the limitations of existing data sources, (ii) the need to balance findings from quantitative and qualitative studies, (iii) the danger that entrepreneurial ecosystems will be just a policy fad, (iv) the narrow focus of policy and research on high tech firms and scale-ups, and (v) the need to balance research approaches between simplified models and a complex systems approach. There is a need for a better understanding of the diversity of policy contexts (level of government, country context) and model of ecosystem governance. A more granulated understanding of ecosystem thinking is required, with greater consideration of the diversity of actors and the institutional context, with more attention given to the heterogeneous nature of places and complex interactions between actors and networks. Looking to the future, the potential of new data sources and methodologies is identified. Future research should give greater consideration to the institutional context to understand how policy can better support entrepreneurial activity and the extent to which specific policies can be replicated elsewhere

Linearisation Instabilities of the Massive Nonsymmetric Gravitational Theory

The massive nonsymmetric gravitational theory is shown to posses a linearisation instability at purely GR field configurations, disallowing the use of the linear approximation in these situations. It is also shown that arbitrarily small antisymmetric sector Cauchy data leads to singular evolution unless an ad hoc condition is imposed on the initial data hypersurface.Comment: 14 pages, IOP style for submission to CQG. Minor changes and additional background material adde