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

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

The heavy quark potential in QCD with 2 flavors of dynamical quarks

We compute the heavy quark potential on configurations generated by the HEMCGC collaboration with dynamical staggered fermions at $6/g^2 = 5.6$ and with dynamical Wilson fermions at $6/g^2 = 5.3$. The computations are done on $16^3 \times 32$ lattices, corresponding to physical sizes of about 1.6 and 2.3 fm, respectively. Up to the distances probed no sign of string breaking is detectable. We also compute the recently proposed scale $r_0$ defined by $r_0^2 F(r_0) = 1.65$.Comment: 8 pages with 3 figures. uuencoded postscript file. FSU-SCRI-94-0

The Nambu--Jona-Lasinio Model of QCD on the Lattice

In an effort to investigate some of the low energy properties of QCD, in particular those related to chiral symmetry breaking, as well as to obtain insights on the behavior of an interacting theory of fermions on the lattice, the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry is studied on the four--dimensional hypercubic lattice using large $N$ techniques and numerical simulations. Naive and Wilson fermions are considered and transparent results are obtained regarding the following: the scalar and pseudoscalar spectrum, the approach to the continuum and chiral limits, the size of the $1/N$ corrections, and the effects of the zero momentum fermionic modes on finite lattices. Also, some interesting observations are made by viewing the model as an embedding theory of the Higgs sector. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL.ps (to get it type: get NJL.ps)Comment: 10 pages, LaTex file. FSU-SCRI-93-12

A Study of the Nambu--Jona-Lasinio Model on the Lattice

We present our full analysis of the two flavor Nambu--Jona-Lasinio model with $SU(2) \times SU(2)$ chiral symmetry on the four--dimensional hypercubic lattice with naive and Wilson fermions. We find that this model is an excellent toy field theory to investigate issues related to lattice QCD. We use the large $N$ approximation to leading order in $1/N$ to obtain non perturbative analytical results over almost the whole parameter range. By using numerical simulations we estimate that the size of the $1/N$ corrections for most of the quantities we consider are small and in this way we strengthen the validity of the leading order large $N$ calculations. We obtain results regarding the approach to the continuum chiral limit, the effects of the zero momentum fermionic modes on finite lattices and the scalar and pseudoscalar spectrum. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your complete E-mail address. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called NJL_long.ps (to get it type: get NJL_long.ps)Comment: 35 pages, LaTex file. (Added section with title: "The zero pion mass line on a finite lattice at large $N$".

On the Dynamics of Light Quarks in QCD

We describe recent results concerning the behavior of lattice QCD with light dynamical Wilson and Staggered quarks. We show that it is possible to reach regions of parameter space with light pions $m_\pi\approx 0.2/a$ using Wilson fermions. If the Hybrid Molecular Dynamics (HMD) algorithm is used with the same parameters it gives incorrect results. We also present preliminary results using a higher-order integration scheme.Comment: 4 pages (all in postscript), proceedings of LAT'9

Effects of spatial size, lattice doubling and source operator on the hadron spectrum with dynamical staggered quarks

We have extended our previous study of the lattice QCD spectrum with 2 flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01 to larger lattices, with better statistics and with additional sources for the propagators. The additional sources allowed us to estimate the $\Delta$ mass and to measure the masses of all mesons whose operators are local in time. These mesons show good evidence for flavor symmetry restoration, except for the masses of the Goldstone and non-Goldstone pions. PCAC is observed in that $m_\pi^2 \propto m_q$, and $f_\pi$ is estimated. Use of undoubled lattices removes problems with the pion propagator found in our earlier work. Previously we found a large change in the nucleon mass at a quark mass of $am_q=0.01$ when we increased the spatial size from 12 to 16. No such effect is observed at the larger quark mass, $am_q=0.025$. Two kinds of wall source were used, and we have found difficulties in getting consistent results for the nucleon mass between the two sources.Comment: 30 pages PostScript fil