Renormalizability of Effective Scalar Field Theory

We present a comprehensive discussion of the consistency of the effective quantum field theory of a single $Z_2$ symmetric scalar field. The theory is constructed from a bare Euclidean action which at a scale much greater than the particle's mass is constrained only by the most basic requirements; stability, finiteness, analyticity, naturalness, and global symmetry. We prove to all orders in perturbation theory the boundedness, convergence, and universality of the theory at low energy scales, and thus that the theory is perturbatively renormalizable in the sense that to a certain precision over a range of such scales it depends only on a finite number of parameters. We then demonstrate that the effective theory has a well defined unitary and causal analytic S--matrix at all energy scales. We also show that redundant terms in the Lagrangian may be systematically eliminated by field redefinitions without changing the S--matrix, and discuss the extent to which effective field theory and analytic S--matrix theory are actually equivalent. All this is achieved by a systematic exploitation of Wilson's exact renormalization group flow equation, as used by Polchinski in his original proof of the renormalizability of conventional $\varphi^4$-theory.Comment: 80 pages, TeX, OUTP-93-23P, CERN-TH.7067/93. Many minor revisions, and several new paragraph

Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Hybrid noiseless subsystems for quantum communication over optical fibers

We derive the general structure of noiseless subsystems for optical radiation contained in a sequence of pulses undergoing collective depolarization in an optical fiber. This result is used to identify optimal ways to implement quantum communication over a collectively depolarizing channel, which in general combine various degrees of freedom, such as polarization and phase, into joint hybrid schemes for protecting quantum coherence.Comment: 5 pages, 1 figur

Linking recorded data with emotive and adaptive computing in an eHealth environment

Telecare, and particularly lifestyle monitoring, currently relies on the ability to detect and respond to changes in individual behaviour using data derived from sensors around the home. This means that a significant aspect of behaviour, that of an individuals emotional state, is not accounted for in reaching a conclusion as to the form of response required. The linked concepts of emotive and adaptive computing offer an opportunity to include information about emotional state and the paper considers how current developments in this area have the potential to be integrated within telecare and other areas of eHealth. In doing so, it looks at the development of and current state of the art of both emotive and adaptive computing, including its conceptual background, and places them into an overall eHealth context for application and development

Operator Relations for SU(3) Breaking Contributions to K and K* Distribution Amplitudes

We derive constraints on the asymmetry a1 of the momentum fractions carried by quark and antiquark in K and K* mesons in leading twist. These constraints follow from exact operator identities and relate a1 to SU(3) breaking quark-antiquark-gluon matrix elements which we determine from QCD sum rules. Comparing our results to determinations of a1 from QCD sum rules based on correlation functions of quark currents, we find that, for a1^\parallel(K*) the central values agree well and come with moderate errors, whereas for a1(K) and a1^\perp(K*) the results from operator relations are consistent with those from quark current sum rules, but come with larger uncertainties. The consistency of results confirms that the QCD sum rule method is indeed suitable for the calculation of a1. We conclude that the presently most accurate predictions for a1 come from the direct determination from QCD sum rules based on correlation functions of quark currents and are given by: a1(K) = 0.06\pm 0.03, a1^\parallel(K*) = 0.03\pm 0.02, a1^\perp(K*) = 0.04\pm 0.03.Comment: 21 page

Expected Inflation and The Sacrifice Ratio

Using inflation forecasts from the OECD Economic Outlook as proxy measures of inflation expectations, we examine the impact of inflation expectations on the sacrifice ratio for 20 OECD countries. The regression analysis considers four different empirical models of the determinants of the sacrifice ratio typically found in the existing literature. The impact of the level of inflation expectations is negative and significant, implying that a higher level of expected inflation is associated with lower sacrifice ratios. This result is consistent with the theoretical role of nominal wage and price rigidities in that reductions in wage and price stickiness diminish the tradeoffs between disinflations and output losses. Interaction effects indicate that higher levels of expected inflation allow policymakers to pursue ‘cold turkey’ inflation reductions even more aggressively. The effect of the change in inflation expectations is negative and significant, implying that faster adjusting inflation expectations are associated with lower sacrifice ratios

Poisson transition rates from time-domain measurements with finite bandwidth

In time-domain measurements of a Poisson two-level system, the observed transition rates are always smaller than those of the actual system, a general consequence of finite measurement bandwidth in an experiment. This underestimation of the rates is significant even when the measurement and detection apparatus is ten times faster than the process under study. We derive here a quantitative form for this correction using a straightforward state-transition model that includes the detection apparatus, and provide a method for determining a system's actual transition rates from bandwidth-limited measurements. We support our results with computer simulations and experimental data from time-domain measurements of quasiparticle tunneling in a single-Cooper-pair transistor.Comment: 4 pages, 5 figure

The Legacy of ERA, Privatization and the Policy Ratchet

This article explores the ways in which the neo-liberal impetus toward the privatization of state schooling signalled in the Education Reform Act 1988 (ERA) has become embedded in the English school system. Four main points are made. First, that ERA itself was of huge strategic rather than substantive importance as far as privatization is concerned. Second, by tracing the lineage of privatization from ERA onwards a 'ratchet' effect of small and incremental policy moves can be identified, which have disseminated, embedded and naturalized privatization within public sector provision. Third, that while privatization has been taken up and taken much further by New Labour than it had been by the Conservatives there are differences between the two sets of governments in the role of privatization in education policy and the role of the state. Fourth, the participation of private providers in the planning and delivery of state services has put the private sector at the very heart of policy. At points the article draws upon interviews conducted with private sector providers. © 2008 Sage Publications