Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.Comment: 4 pages, 1 figur

The sustainability of public health interventions in schools: a systematic review

Background: The sustainability of school-based health interventions after external funds and/or other resources end has been relatively unexplored in comparison to health care. If effective interventions discontinue, new practices cannot reach wider student populations and investment in implementation is wasted. This review asked: What evidence exists about the sustainability of school-based public health interventions? Do schools sustain public health interventions once start-up funds end? What are the barriers and facilitators affecting the sustainability of public health interventions in schools in high-income countries? Methods: Seven bibliographic databases and 15 websites were searched. References and citations of included studies were searched, and experts and authors were contacted to identify relevant studies. We included reports published from 1996 onwards. References were screened on title/abstract, and those included were screened on full report. We conducted data extraction and appraisal using an existing tool. Extracted data were qualitatively synthesised for common themes, using May's General Theory of Implementation (2013) as a conceptual framework. Results: Of the 9677 unique references identified through database searching and other search strategies, 24 studies of 18 interventions were included in the review. No interventions were sustained in their entirety; all had some components that were sustained by some schools or staff, bar one that was completely discontinued. No discernible relationship was found between evidence of effectiveness and sustainability. Key facilitators included commitment/support from senior leaders, staff observing a positive impact on students' engagement and wellbeing, and staff confidence in delivering health promotion and belief in its value. Important contextual barriers emerged: the norm of prioritising educational outcomes under time and resource constraints, insufficient funding/resources, staff turnover and a lack of ongoing training. Adaptation of the intervention to existing routines and changing contexts appeared to be part of the sustainability process. Conclusions: Existing evidence suggests that sustainability depends upon schools developing and retaining senior leaders and staff that are knowledgeable, skilled and motivated to continue delivering health promotion through ever-changing circumstances. Evidence of effectiveness did not appear to be an influential factor. However, methodologically stronger primary research, informed by theory, is needed. Trial registration: The review was registered on PROSPERO: CRD42017076320, Sep. 2017

Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics

The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular $\hbar\downarrow0$ asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the $\hbar$ coefficients recursively. The Heisenberg--Weyl description of evolution involves no essential singularity in $\hbar$, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics or Maslov indices.Comment: 50, MANIT-94-0

Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local correlations. In the chirally symmetric phase, the local correlations in the bulk of the spectrum are still described by random matrix theory, and we investigate the dependence of the bulk Thouless energy on the simulation parameters. At and above the critical point, the properties of the low-lying Dirac eigenvalues depend on the $Z_3$-phase of the Polyakov loop. In the real phase, they are no longer described by chiral random matrix theory. We also investigate the localization properties of the Dirac eigenvectors in the different $Z_3$-phases.Comment: Lattice 2000 (Finite Temperature), 5 page

Forty-eight-inch lidar aerosol measurements taken at the Langley Research Center, May 1974 to December 1987

A ground based lidar system located at NASA Langley Research Center in Hampton, Va., was used to obtain high resolution vertical profiles of the stratospheric and upper tropospheric aerosol since 1974. More than 200 measurements obtained at a wavelength of 0.6943 microns during 1974 to 1987 are summarized. Plots of peak backscatter mixing ratio and integrated backscatter vs time are presented for the entire measurement sequence. The plots highlight the influence of several major volcanic eruptions on the long term stratospheric aerosol layer. In particular, the eruptions of El Chichon in late Mar. to early Apr. 1982, produced a massive aerosol layer. Aerosol enhancement from El Chichon reached Hampton, Va. by May 1982, with a scattering ratio of approx. 50 detected on Jul. 1, 1982. In addition, scattering ratio profiles for June 1982 to December 1987, along with tables containing numerical values of the backscatter ratio and backscattering function versus altitude, are included to further describe the upper tropospheric and stratospheric aerosol layer. A 14 year summary is presented, in a ready to use format, of lidar observations at a fixed midlatitude location to be used for further study

Spectrum of the U(1) staggered Dirac operator in four dimensions

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.Comment: 5 pages, 3 figure

Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations. In the fixed point the diffeomorphism and Weyl transformations generate an infinite algebraic structure of D-Dimensional conformal field theory models. The Wilson expansion and crossing symmetry enable to obtain sum rules for dimensions of composite operators and Wilson coefficients.Comment: 16 page