Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved spacetime are the canonical commutation relations, imposed on the field operators evaluated at a global Cauchy surface. In the algebraic formulation of linear quantum field theory, the canonical commutation relations are restated in terms of a well-defined symplectic structure on the space of smooth solutions, and the local field algebra is constructed as the Weyl algebra associated to this symplectic vector space. When spacetime is not globally hyperbolic, e.g. when it contains naked singularities or closed timelike curves, a global Cauchy surface does not exist, and there is no obvious way to formulate the canonical commutation relations, hence no obvious way to construct the field algebra. In a paper submitted elsewhere, we report on a generalization of the algebraic framework for quantum field theory to arbitrary topological spaces which do not necessarily have a spacetime metric defined on them at the outset. Taking this generalization as a starting point, in this paper we give a prescription for constructing the field algebra of a (massless or massive) Klein-Gordon field on an arbitrary background spacetime. When spacetime is globally hyperbolic, the theory defined by our construction coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4

Families of spherical caps: spectra and ray limit

We consider a family of surfaces of revolution ranging between a disc and a hemisphere, that is spherical caps. For this family, we study the spectral density in the ray limit and arrive at a trace formula with geodesic polygons describing the spectral fluctuations. When the caps approach the hemisphere the spectrum becomes equally spaced and highly degenerate whereas the derived trace formula breaks down. We discuss its divergence and also derive a different trace formula for this hemispherical case. We next turn to perturbative corrections in the wave number where the work in the literature is done for either flat domains or curved without boundaries. In the present case, we calculate the leading correction explicitly and incorporate it into the semiclassical expression for the fluctuating part of the spectral density. To the best of our knowledge, this is the first calculation of such perturbative corrections in the case of curvature and boundary.Comment: 28 pages, 7 figure

DPP9 is a novel component of the N-end rule pathway targeting the tyrosine kinase Syk.

The aminopeptidase DPP9 removes dipeptides from N-termini of substrates having a proline or alanine in second position. Although linked to several pathways including cell survival and metabolism, the molecular mechanisms underlying these outcomes are poorly understood. We identified a novel interaction of DPP9 with Filamin A, which recruits DPP9 to Syk, a central kinase in B-cell signalling. Syk signalling can be terminated by degradation, requiring the ubiquitin E3 ligase Cbl. We show that DPP9 cleaves Syk to produce a neo N-terminus with serine in position 1. Pulse-chases combined with mutagenesis studies reveal that Ser1 strongly influences Syk stability. Furthermore, DPP9 silencing reduces Cbl interaction with Syk, suggesting that DPP9 processing is a prerequisite for Syk ubiquitination. Consistently, DPP9 inhibition stabilizes Syk, thereby modulating Syk signalling. Taken together, we demonstrate DPP9 as a negative regulator of Syk and conclude that DPP9 is a novel integral aminopeptidase of the N-end rule pathway

Radiation from a D-dimensional collision of shock waves: first order perturbation theory

We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in D dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and a perturbative framework to compute the metric in the future of the collision is setup. The geometry is given, in first order perturbation theory, as an integral solution, in terms of initial data on the null surface where the strong shock has support. We then extract the radiation emitted in the collision by using a D-dimensional generalisation of the Landau-Lifschitz pseudo-tensor and compute the percentage of the initial centre of mass energy epsilon emitted as gravitational waves. In D=4 we find epsilon=25.0%, in agreement with the result of D'Eath and Payne. As D increases, this percentage increases monotonically, reaching 40.0% in D=10. Our result is always within the bound obtained from apparent horizons by Penrose, in D=4, yielding 29.3%, and Eardley and Giddings, in D> 4, which also increases monotonically with dimension, reaching 41.2% in D=10. We also present the wave forms and provide a physical interpretation for the observed peaks, in terms of the null generators of the shocks.Comment: 27 pages, 11 figures; v2 some corrections, including D dependent factor in epsilon; matches version accepted in JHE

Light-Front Quantisation as an Initial-Boundary Value Problem

In the light front quantisation scheme initial conditions are usually provided on a single lightlike hyperplane. This, however, is insufficient to yield a unique solution of the field equations. We investigate under which additional conditions the problem of solving the field equations becomes well posed. The consequences for quantisation are studied within a Hamiltonian formulation by using the method of Faddeev and Jackiw for dealing with first-order Lagrangians. For the prototype field theory of massive scalar fields in 1+1 dimensions, we find that initial conditions for fixed light cone time {\sl and} boundary conditions in the spatial variable are sufficient to yield a consistent commutator algebra. Data on a second lightlike hyperplane are not necessary. Hamiltonian and Euler-Lagrange equations of motion become equivalent; the description of the dynamics remains canonical and simple. In this way we justify the approach of discretised light cone quantisation.Comment: 26 pages (including figure), tex, figure in latex, TPR 93-

Quantum ergodicity for graphs related to interval maps

We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2 functions on the interval. The proof is based on the periodic orbit expansion of a majorant of the quantum variance. Specifically, given a one-dimensional, Lebesgue-measure-preserving map of an interval, we consider an increasingly refined sequence of partitions of the interval. To this sequence we associate a sequence of graphs, whose directed edges correspond to elements of the partitions and on which the classical dynamics approximates the Perron-Frobenius operator corresponding to the map. We show that, except possibly for subsequences of density 0, the eigenstates of the quantum graphs equidistribute in the limit of large graphs. For a smaller class of observables we also show that the Egorov property, a correspondence between classical and quantum evolution in the semiclassical limit, holds for the quantum graphs in question.Comment: 20 pages, 1 figur

Long-term efficacy, tolerability and overall survival in patients with platinum-sensitive, recurrent high-grade serous ovarian cancer treated with maintenance olaparib capsules following response to chemotherapy

BACKGROUND: In Study 19, maintenance monotherapy with olaparib significantly prolonged progression-free survival vs placebo in patients with platinum-sensitive, recurrent high-grade serous ovarian cancer. METHODS: Study 19 was a randomised, placebo-controlled, Phase II trial enrolling 265 patients who had received at least two platinum-based chemotherapy regimens and were in complete or partial response to their most recent regimen. Patients were randomised to olaparib (capsules; 400 mg bid) or placebo. We present long-term safety and final mature overall survival (OS; 79% maturity) data, from the last data cut-off (9 May 2016). RESULTS: Thirty-two patients (24%) received maintenance olaparib for over 2 years; 15 (11%) did so for over 6 years. No new tolerability signals were identified with long-term treatment and adverse events were generally low grade. The incidence of discontinuations due to adverse events was low (6%). An apparent OS advantage was observed with olaparib vs placebo (hazard ratio 0.73, 95% confidence interval 0.55‒0.95, P = 0.02138) irrespective of BRCA1/2 mutation status, although the predefined threshold for statistical significance was not met. CONCLUSIONS: Study 19 showed a favourable final OS result irrespective of BRCA1/2 mutation status and unprecedented long-term benefit with maintenance olaparib for a subset of platinum-sensitive, recurrent ovarian cancer patients

Plasma synthesis of single crystal silicon nanoparticles for novel electronic device applications

Single-crystal nanoparticles of silicon, several tens of nm in diameter, may be suitable as building blocks for single-nanoparticle electronic devices. Previous studies of nanoparticles produced in low-pressure plasmas have demonstrated the synthesis nanocrystals of 2-10 nm diameter but larger particles were amorphous or polycrystalline. This work reports the use of a constricted, filamentary capacitively coupled low-pressure plasma to produce single-crystal silicon nanoparticles with diameters between 20-80 nm. Particles are highly oriented with predominant cubic shape. The particle size distribution is rather monodisperse. Electron microscopy studies confirm that the nanoparticles are highly oriented diamond-cubic silicon.Comment: accepted for publication in Plasma Physics and Controlled Fusion, scheduled for Dec. 2004 F