Path Integrals and Voronin's Theorem on the Universality of the Riemann Zeta Function

We explore a new approach to the path integral for a latticized quantum theory. This talk is based on work with N. Khuri and H. Ren

On the Parity-Flavor-Breaking Phase in QCD With Two Flavors of Wilson Fermions

We present further data in search of a parity-flavor-breaking phase in simulations of dynamical QCD with two flavors of light Wilson fermions in the strong coupling region. This is done on lattice sizes of 4^4 an up to 10^4 for a variety of values of beta and kappa as well as the coefficient, h, of an explicit breaking term included in the action. We confirm the existence of a region in the beta-kappa plane where such a phase exists at beta=6/g^2 smaller than 5.0 and above kappa_c.Comment: 3 pages latex209 with 3 postscript figures included by epsf, contribution to LAT'9

P-wave meson properties with Wilson quarks

We describe two calculations involving P-wave mesons made of Wilson quarks: the strong coupling constant $\alpha_s$ in the presence of two flavors of light dynamical fermions and the mass and decay constant of the $a_1$ meson.Comment: Poster presented at Lattice '94, September 27--October 1, 1994, Bielefeld, Germany (no changes to manuscript, but correction of Authors list above

SCRI Results With the Tadpole-Improved Clover Action

We compare light hadron spectroscopy using the Wilson and Clover fermionic actions. We show that a Clover coefficient chosen using tadpole-improved tree-level perturbation theory effectively eliminates the O(a) discretization errors present in the Wilson action. We find that discretization errors in light spectroscopy for both the Wilson and Clover actions are characterized by an energy scale mu of about 200-300 MeV, indicating that these errors can be reduced to the 5% level by using the Clover action at an inverse lattice spacing of about 1.3 GeV.Comment: Talk presented at the International Workshop on Lattice QCD On Parallel Computers, University of Tsukuba, March 10-15 1997. 9 LaTex pages plus 6 postscript figures, uses espcrc2.st

A new method to measure the chiral condensate in lattice QCD using Wilson fermions

Parity and flavor symmetry is not broken in QCD. Using this fact, we propose a new method to measure the chiral condensate in lattice QCD using Wilson fermions with an operator that breaks parity and flavor in addition to the chiral symmetry.Comment: 9 pages, LaTeX, no figure

Spectral flow, condensate and topology in lattice QCD

We study the spectral flow of the Wilson-Dirac operator H(m) with and without an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice gauge field ensembles in the range $0\le m \le 2$. We have used ensembles generated from the Wilson gauge action, an improved gauge action, and several two-flavor dynamical quark ensembles. Two regions in $m$ provide a generic characterization of the spectrum. In region I defined by $m\le m_1$, the spectrum has a gap. In region II defined by $m_1\le m \le 2$, the gap is closed. The level crossings in H(m) that occur in region II correspond to localized eigenmodes and the localization size decreases monotonically with the crossing point down to a size of about one lattice spacing. These small modes are unphysical, and we find the topological susceptibility is relatively stable in the part of region II where the small modes cross. We argue that the lack of a gap in region II is expected to persist in the infinite volume limit at any gauge coupling. The presence of a gap is important for the implementation of domain wall fermions.Comment: 30 pages latex with 13 postscript figures included by epsf. Expanded discussion on domain wall fermions. Two figures have been bitmapped to reduce size. Originals are in http://www.scri.fsu.edu/~edwards/su3_to

Evidence for hard chiral logarithms in quenched lattice QCD

We present the first direct evidence that quenched QCD differs from full QCD in the chiral ($m_q \rightarrow 0$) limit, as predicted by chiral perturbation theory, from our quenched lattice QCD simulations at $\beta = 6/g^2 = 6.0$. We measured the spectrum of light hadrons on $16^3 \times 64$, $24^3 \times 64$ and $32^3 \times 64$, using staggered quarks of masses $m_q=0.01$, $m_q=0.005$ and $m_q=0.0025$. The pion masses showed clear evidence for logarithmic violations of the PCAC relation $m_{\pi}^2 \propto m_q$, as predicted by quenched chiral perturbation theory. The dependence on spatial lattice volume precludes this being a finite size effect. No evidence was seen for such chiral logarithms in the behaviour of the chiral condensate $\langle\bar{\psi}\psi\rangle$.Comment: 10 pages, 4 figures, uuencoded compressed postscript fil