A new simulation algorithm for lattice QCD with dynamical quarks

A previously introduced multi-boson technique for the simulation of QCD with dynamical quarks is described and some results of first test runs on a $6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.Comment: 7 pages, postscript file (166 KB

Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction

Towards Weyl fermions on the lattice without artefacts

In spite of the breakthrough in non-perturbative chiral gauge theories during the last decade, the present formulation has stubborn artefacts. Independently of the fermion representation one is confronted with unwanted CP violation and infinitely many undetermined weight factors. Renormalization group identifies the culprit. We demonstrate the procedure on Weyl fermions in a real representation

Non-perturbative quark mass renormalization

We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\Lambda$--parameter in this theory with completely controlled errors.Comment: Talk given at LATTICE '97, 6 pages, Latex source, 7 eps figures, needs epsfi

Ginsparg-Wilson relation and the overlap formula

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.Comment: 4 pages, plain tex, no figure

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

O(a)O(a) Improvement of Nucleon Matrix Elements

We report on preliminary results of a high statistics quenched lattice QCD calculation of nucleon matrix elements within the Symanzik improvement programme. Using the recently determined renormalisation constants from the Alpha Collaboration we present a fully non-pertubative calculation of the forward nucleon axial matrix element with $O(a)$ lattice artifacts completely removed. Runs are made at $\beta=6.0$ and $\beta=6.2$, in an attempt to check scaling and $O(a^2)$ effects. We shall also briefly describe results for $$, the matrix element of a higher derivative operator.Comment: 3 pages, Latex, 4 figures, epsf.sty and espcrc2.sty needed, Talk given at LATTICE97. Figure 4 correcte

Non-perturbative renormalisation and improvement of the local vector current for quenched and unquenched Wilson fermions

By considering the local vector current between nucleon states and imposing charge conservation, we determine its renormalisation constant and quark mass improvement coefficient for Symanzik $O(a)$ improved Wilson fermions. The computation is first performed for quenched fermions (and for completeness also with unimproved fermions) and compared against known results. The two-flavour unquenched case is then considered.Comment: 15 pages, 5 figures, Latex, Final versio

Perturbation Calculation of the Axial Anomaly of a Ginsparg-Wilson lattice Dirac operator

A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially-local, doublers-free, and has correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge backgroun

Renormalisation of one-link quark operators for overlap fermions with L\"uscher-Weisz gauge action

We compute lattice renormalisation constants of one-link quark operators ({\it i.e.} operators with one covariant derivative) for overlap fermions and L\"uscher-Weisz gauge action in one-loop perturbation theory. Among others, such operators enter the calculation of moments of polarised and unpolarised hadron structure functions. Results are given for \beta=8.45, \beta=8.0 and mass parameter \rho=1.4, which are commonly used in numerical simulations. We apply mean field (tadpole) improvement to our results.Comment: 13 pages, 1 figur