arXiv subjects
Publications and source records attributed to M. Testa.
We show that a modification of the BRST lattice quantization allows to circumvent an old paradox, formulated by Neuberger, related to lattice Gribov copies and non-perturbative BRST invariance. In the continuum limit the usual BRST formulation is recovered.
We address the problem of defining the gauge four-potential on the lattice, in terms of the natural link variables. Different regularized definitions are shown, through non perturbative numerical computation, to converge towards the same continuum renormalized limit.
We present a general analysis of the field theoretical properties which guarantee the recovery, at the renormalized level, of symmetries broken by regularization. We also discuss the anomalous case.
We outline two methods of constructing improved composite operators using Wilson fermions.
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the non-decay amplitude.
A general review is presented on the problem of non perturbative computation of the $K\toππ$ transition amplitude.
We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass, leaving only errors of $O(a^2)$. The method exploits the fact that chiral symmetry is restored at short distances. By imposing this requirement on correlation functions of improved lattice operators at short distances, the coefficients which appear in these operators can be determined. The method is an extension of the improvement program of the ALPHA collaboration, which, up to now, has only been applicable in the chiral limit. The extension to quarks with non-zero masses is particularly important for applications in heavy quark physics.
Lattice QCD should allow a derivation of the $ΔI=1/2$ rule from first principles, but numerical calculations to date have been plagued by a variety of problems. After a brief review of these problems, we present several new methods for calculating $K\toππ$ amplitudes. These are designed for Wilson fermions, though they can be used also with staggered fermions. They all involve a non-perturbative determination of matching coefficients. We show how problems of operator mixing can be greatly reduced by using point-split hadronic currents, and how CP violating parts of the $K\toππ$ amplitudes can be calculated by introducing a fake top quark. Many of the methods can also be applied to the calculation of two body non-leptonic B-meson decays.
We discuss the application of the MPSTV non-perturbative method \cite{NPM} to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the $ΔI=1/2$ rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the $B_K$ parameter.
We propose a general renormalization method, which avoids completely the use of lattice perturbation theory. We present the results from its numerical applications to two-fermion operators on a $16^3 \times 32$ lattice, at $β=6.0$.
We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of $QCD$, on a $16^3 \times 32$ lattice, at $β=6.0$. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.
We present the results of two high-statistics studies of the gluon propagator in the Landau gauge, at $β=6.0$, on different lattice volumes. The dependence of the propagator on the momenta is well described by the expression $G(k^2) = \Big[ M^2+Z\cdot k^2(k^2/ Λ^2)^η)\Big]^{-1}$. We obtain a precise determination of $η=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit.
The problem of causality is analyzed in the context of Local Quantum Field Theory. Contrary to recent claims, it is shown that apparent noncausal behaviour is due to a lack of the notion of sharp localizability for a relativistic quantum system. (Replaced corrupted file)