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The dominant cutoo eeects in lattice QCD with Wilson quarks are proportional to the lattice spacing a. In particular, the isovector axial current satisses the PCAC relation only up to such eeects. Following a suggestion of Symanzik, they can be cancelled by adding local O(a) correction terms to the action and the axial current. We here address a number of(More)
Following Symanzik we argue that the Schrödinger 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 Schrödinger functional is, moreover, accessible to numerical simulations. It may hence be used to study the scaling properties of the theory and in(More)
Lattice QCD with Wilson quarks and a chirally twisted mass term represents a promising alternative regularization of QCD, which does not suffer from unphysical fermion zero modes. We show how the correlation functions of the renormalized theory are related to the theory with a standard parameterization of the mass term. In particular we discuss the(More)
We present results at one-loop order of perturbation theory for various improvement coeecients 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 renor-malization scheme we also obtain the coeecients of the O(a)(More)
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(More)
In the presence of a static quark-antiquark pair, the spectrum of the low-lying states in SU(N) gauge theories is discrete and likely to be described, at large quark separations r, by an effective string theory. The expansion of the excitation energies in powers of 1/r, which derives from the latter, involves an increasing number of unknown couplings that(More)
A non-perturbative nite-size scaling technique is used to study the evolution of the running coupling (in a certain adapted scheme) in the SU(3) Yang-Mills theory. At low energies contact is made with the fundamental dynamical scales, such as the string tension K, while at larger energies the coupling is shown to evolve according to perturbation theory. In(More)
S-matrices describing the scattenng of sohtons belortgmg to the fundamental representation of U(n) are classified A variety of two-&menslonal field theories have the property of being completely mtegrable at the classical level and describe Interactions of solitons. In the cases investigated so far, the most studied example being the sine-Gordon theory(More)