Locality and exponential error reduction in numerical lattice gauge theory

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm^2.Comment: Plain TeX source, 18 pages, figures include

One-loop renormalization factors and mixing coeffecients of bilinear quark operators for improved gluon and quark actions

We calculate one-loop renormalization factors and mixing coefficients of bilinear quark operators for a class of gluon actions with six-link loops and O(a)-improved quark action. The calculation is carried out by evaluating on-shell Green's functions of quarks and gluons in the standard perturbation theory. We find a general trend that finite parts of one-loop coefficients are reduced approximately by a factor two for the renormalization-group improved gluon actions compared with the case of the standard plaquette gluon action.Comment: LATTICE98(improvement), 3 page

Physical and Monetary Input-Output Analysis: What Makes the Difference?

A recent paper in which embodied land appropriation of exports was calculated using a physical input-output model (Ecological Economics 44 (2003) 137-151) initiated a discussion in this journal concerning the conceptual differences between input-output models using a coefficient matrix based on physical input-output tables (PIOTs) in a single unit of mass and input-output models using a coefficient matrix based on monetary input-output tables (MIOTs) extended by a coefficient vector of physical factor inputs per unit of output. In this contribution we argue that the conceptual core of the discrepancies found when comparing outcomes obtained using physical vs. monetary input-output models lies in the assumption of prices and not in the treatment of waste as has been claimed (Ecological Economics 48 (2004) 9-17). We first show that a basic static input-output model with the coefficient matrix derived from a monetary input-output table is equivalent to one where the coefficient matrix is derived from an input-output table in physical units provided that the assumption of unique sectoral prices is satisfied. We then illustrate that the physical input-output table that was used in the original publication does not satisfy the assumption of homogenous sectoral prices, even after the inconsistent treatment of waste in the PIOT is corrected. We show that substantially different results from the physical and the monetary models in fact remain. Finally, we identify and discuss possible reasons for the observed differences in sectoral prices and draw conclusions for the future development of applied physical input-output analysis.

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1,2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacing a. Based on the generalised transfer matrix, we define the tmQCD Schrodinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.Comment: 31 pages latex, no figure

Further results on O(a) improved lattice QCD to one-loop order of perturbation theory

We present results at one-loop order of perturbation theory for various improvement coefficients in on-shell O($a$) improved lattice QCD. In particular we determine the additive counterterm required for on-shell improvement of the isovector vector current. Employing a general mass-independent renormalization scheme we also obtain the coefficients of the O($a$) counterterms which are proportional to the quark mass in the improved isovector pseudo-scalar, axial vector and vector operators. In the latter case a comparison with a recent non-perturbative study is made.Comment: 24 pages plain TeX, 2 postscript figures, macros and format files include