Message passing on the QCDSP supercomputer

The QCDSP machines were designed for lattice gauge calculations. For planning it is crucial to explore this architecture for other computationally intensive tasks. Here I describe an implementation of a simple message passing scheme. With the objective being simplicity, I introduce a small number of generic functions for manipulating a large data set spread over the machine. I test the scheme on three applications: a fast Fourier transform, arbitrary dimension SU(N) pure lattice gauge theory, and the manipulation of Fermionic Fock states through a distributed hash table. These routines compile both on QCDSP and a Unix workstation.Comment: LATTICE99(Algorithms and Machines) - 3 page

Wilson Fermions at finite temperature

I conjecture on the phase structure expected for lattice gauge theory with two flavors of Wilson fermions, concentrating on large values of the hopping parameter. Numerous phases are expected, including the conventional confinement and deconfinement phases, as well as an Aoki phase with spontaneous breaking of flavor and parity and a large hopping phase corresponding to negative quark masses.Comment: 9 pages, 4 figures. Talk at Brookhaven Theory Workshop on Relativistic Heavy Ions, July 1996 Replacement contains added reference and acknowledgemen

Quark Masses and Chiral Symmetry

I discuss the global structure of the strongly interacting gauge theory of quarks and gluons as a function of the quark masses and the CP violating parameter $\theta$. I concentrate on whether a first order phase transition occurs at $\theta=\pi.$ I show why this is expected when multiple flavors have a small degenerate mass. This transition can be removed by sufficient flavor-breaking. I speculate on the implications of this structure for Wilson's lattice fermions.Comment: compressed postscript file, 20 pages with 10 figures. Also available at http://penguin.phy.bnl.gov/www/papers/BNL-61796.ps.

The Early Days of Lattice Gauge Theory

I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles. I wrap up with some challenges for the future.Comment: 9 pages, 3 figures, contribution to conference "The Monte Carlo method in the physical sciences: Celebrating the 50th anniversary of the Metropolis algorithm," Los Alamos, June 9-11, 200

The lattice and quantized Yang-Mills theory

Quantized Yang-Mills fields lie at the heart of our understanding of the strong nuclear force. To understand the theory at low energies, we must work in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.Comment: 13 pages, 3 figures. Contribution to the Conference on 60 Years of Yang-Mills Gauge Field Theories, 25-28 May 2015. arXiv admin note: substantial text overlap with arXiv:hep-lat/0406007, arXiv:hep-lat/0306024, arXiv:hep-lat/001004

Direct simulations of small multi-fermion systems

I explore computer simulations of the dynamics of small multi-fermion lattice systems. The method is more general, but I concentrate on Hubbard type models where the fermions hop between a small number of connected sites. I use the natural mapping of fermion occupation numbers onto computer bits. Signs from fermion interchange are reduced to bit counting. The technique inherently requires computer resources growing exponentially with the system volume; so, it restricted to modestly small systems. Large volume results would require combining these techniques with further approximations, perhaps in a recursive renormalization group manner.Comment: 17 pages, 9 figures, revtex

Quark masses and strong CP violation

Two flavor QCD involves three independent mass parameters for which non-perturbative effects are not universal. This precludes matching lattice and perturbative results for non-degenerate quarks and eliminates a vanishing up quark mass as a viable solution to the strong CP problem.Comment: 1 page, 1 figure; poster contribution to the conference "Quark confinement and the hadron spectrum IX," August 30 - September 10, 201

Partial quenching and chiral symmetry breaking

Partially quenched chiral perturbation theory assumes that valence quarks propagating on gauge configurations prepared with sea quarks of different masses will form a chiral condensate as the valence quark mass goes to zero. I present a counterexample involving non-degenerate sea quarks where the valence condensate does not form.Comment: 4 pages, 1 figure. Contribution to the 32nd International Symposium on Lattice Field Theory 23-28 June, 2014, Columbia Universit