79 research outputs found
Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
We perform a comparison between different lattice regularizations of the
Dirac operator for massless fermions in the framework of the single and two
flavor Schwinger model. We consider a) the Wilson-Dirac operator at the
critical value of the hopping parameter; b) Neuberger's overlap operator; c)
the fixed point operator. We test chiral properties of the spectrum, dispersion
relations and rotational invariance of the mesonic bound state propagators.Comment: Revised version; 13 pages (LaTeX), 3 figures (EPS
Topological Charge and the Spectrum of the Fermion Matrix in Lattice-QED_2
We investigate the interplay between topological charge and the spectrum of
the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo
simulations with dynamical fermions. A new theorem on the spectral
decomposition of the fermion matrix establishes that its real eigenvalues (and
corresponding eigenvectors) play a role similar to the zero eigenvalues (zero
modes) of the Dirac operator in continuous background fields. Using numerical
techniques we concentrate on studying the real part of the spectrum. These
results provide new insights into the behaviour of physical quantities as a
function of the topological charge. In particular we discuss fermion
determinant, effective action and pseudoscalar densities.Comment: 33 pages, 10 eps-figures; reference adde
Constructing Improved Overlap Fermions in QCD
We describe an explicit construction of approximate Ginsparg-Wilson fermions
for QCD. We use ingredients of perfect action origin, and further elements. The
spectrum of the lattice Dirac operator reveals the quality of the
approximation. We focus on beta =6 for optimisation. Such fermions are intended
to be inserted into the overlap formula. Hence we also test the speed of
convergence under polynomial evaluation of the overlap formula.Comment: 5 pages, poster presented at Lattice 2000 (Improvement and
Renormalisation
Chiral symmetry in the 2-flavour lattice Schwinger model
We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion
species of identical mass. In the simulation we are using Wilson fermions where
chiral symmetry is explicitly broken. Since there is no known simple order
parameter it is non-trivial to identify the critical line of the chiral phase
transition. We therefore need to find observables which allow an identification
of a possible restoration of chiral symmetry. We utilize the PCAC-relations in
order to identify the critical coupling, where chiral symmetry is restored.Comment: 3 pages (LaTeX), 4 figures (EPS
The Consequences of Non-Normality
The non-normality of Wilson-type lattice Dirac operators has important consequences - the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D^{-1} and we prove that due to the gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator
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