The Schr\"odinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories

Following Symanzik we argue that the Schr\"odinger functional in lattice gauge theories without matter fields has a well-defined continuum limit. Due to gauge invariance no extra counter terms are required. The Schr\"odinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in particular the evolution of the renormalized gauge coupling from low to high energies. A concrete proposition along this line is made and the necessary perturbative analysis of the Schr\"odinger functional is carried through to 1-loop order.Comment: 68 page

International comparison of health care carbon footprints

Climate change confronts the health care sector with a dual challenge. Accumulating climate impacts are putting an increased burden on the service provision of already stressed health care systems in many regions of the world. At the same time, the Paris agreement requires rapid emission reductions in all sectors of the global economy to stay well below the 2 °C target. This study shows that in OECD countries, China, and India, health care on average accounts for 5% of the national CO2 footprint making the sector comparable in importance to the food sector. Some countries have seen reduced CO2 emissions related to health care despite growing expenditures since 2000, mirroring their economy wide emission trends. The average per capita health carbon footprint across the country sample in 2014 was 0.6 tCO2, varying between 1.51 tCO2/cap in the US and 0.06 tCO2/cap in India. A statistical analysis shows that the carbon intensity of the domestic energy system, the energy intensity of the domestic economy, and health care expenditure together explain half of the variance in per capita health carbon footprints. Our results indicate that important leverage points exist inside and outside the health sector. We discuss our findings in the context of the existing literature on the potentials and challenges of reducing GHG emissions in the health and energy sector.Austrian Climate Research ProgramPeer Reviewe

International comparison of health care carbon footprints

Climate change confronts the health care sector with a dual challenge. Accumulating climate impacts are putting an increased burden on the service provision of already stressed health care systems in many regions of the world. At the same time, the Paris agreement requires rapid emission reductions in all sectors of the global economy to stay well below the 2 °C target. This study shows that in OECD countries, China, and India, health care on average accounts for 5% of the national CO2 footprint making the sector comparable in importance to the food sector. Some countries have seen reduced CO2 emissions related to health care despite growing expenditures since 2000, mirroring their economy wide emission trends. The average per capita health carbon footprint across the country sample in 2014 was 0.6 tCO2, varying between 1.51 tCO2/cap in the US and 0.06 tCO2/cap in India. A statistical analysis shows that the carbon intensity of the domestic energy system, the energy intensity of the domestic economy, and health care expenditure together explain half of the variance in per capita health carbon footprints. Our results indicate that important leverage points exist inside and outside the health sector. We discuss our findings in the context of the existing literature on the potentials and challenges of reducing GHG emissions in the health and energy sector

Non-perturbative renormalization of lattice QCD at all scales

A general strategy to solve the non-perturbative renormalization problem in lattice QCD, using finite-size techniques and numerical simulations, is described. As an illustration we discuss the computation of the axial current normalization constant, the running coupling at zero quark masses and the scale evolution of the renormalized axial density. The non-perturbative calculation of O(a) correction terms (as they appear in Symanzik's improvement programme) is another important field of application.Comment: 14 pages, uuencoded gzipped postscript fil

Some new results in O(a) improved lattice QCD

It is shown how on-shell O(a) improvement can be implemented non-perturbatively in lattice QCD with Wilson quarks. Improvement conditions are obtained by requiring the PCAC relation to hold exactly in certain matrix elements. These are derived from the QCD Schrödinger functional which enables us to simulate directly at vanishing quark masses. In the quenched approximation and for bare couplings in the range $0\leq g_0\leq 1$, we determine the improved action, the improved axial current, the additive renormalization of the quark mass and the isospin current normalization constants Z_A and Z_V

Finite size scaling and triviality of \phi^4 theory on an antiperiodic torus

Worm methods to simulate the Ising model in the Aizenman random current representation including a low noise estimator for the connected four point function are extended to allow for antiperiodic boundary conditions. In this setup several finite size renormalization schemes are formulated and studied with regard to the triviality of \phi^4 theory in four dimensions. With antiperiodicity eliminating the zero momentum Fourier mode a closer agreement with perturbation theory is found compared to the periodic torus.Comment: 20 pages, 3 double-figures, 6 table

Two Loop Computation of the Schroedinger Functional in Lattice QCD

We compute the Schroedinger functional (SF) for the case of lattice QCD with Wilson fermions (with and without SW improvement) at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size techniques with negligible systematic errors. In addition our results enable the implementation of two-loop O(a) improvement in SF-simulations.Comment: 30 pages, numerical changes in eqs.(A.9), (A.10), (5.6), (5.9), (5.12) due to the revision of hep-lat/9801007v2 (Christou et al.

Triviality of ϕ44\phi^4_4 theory: small volume expansion and new data

We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the equivalent all-order strong coupling reformulation. Ordinary renormalized perturbation theory is found to work marginally at z=2 and and to fail at z=1. By exactly integrating over the constant field mode we set up a renormalized expansion in z and compute three nontrivial orders. These results reasonably agree with the numerical data at small z. In the new expansion, the universal continuum limit exists as expected from multiplicative renormalizability. The triviality scenario is corroborated with significant precision.Comment: 27 pages, 7 figures, 4 table

First results on the running coupling in QCD with two massless flavours

We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.Comment: 14 pages, 5 figures, 3 tables, some changes in the data analysis after discovery and correction of an error in Nucl. Phys. B 525, 387 (1998) by C. Christou et al. (hep-lat/9801007v2, Erratum to appear

Schr"odinger functional at negative flavour number

The scaling of the Schr"odinger functional coupling is studied numerically and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved bosonic spinor field. This corresponds to QCD with minus two light flavours and is used as a numerically less costly test case for real QCD. A suitable algorithm is developed, and the influence of the matter fields on the continuum limit and the lattice artefacts are studied in detail.Comment: 24 pages, 7 figures, small textual change