557 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
New approximate solutions of the Ginsparg-Wilson equation - tests in 2-d
A new method for finding approximate solutions of the Ginsparg-Wilson
equation is tested in 2-d. The Dirac operator is first constructed and then
used in a dynamical simulation of the 2-flavor Schwinger model. We find a very
small mass of the pi-particle implying almost chirally symmetric fermions. The
generalization of our method to 4-d is straightforward.Comment: Revised version (to appear in Physics Letters B); references added
and regrouped; new comment on finite size effect
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
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