The problems involved in simulating a liquid on a MIMD and on a SIMD computer are analysed and compared, with specific reference to the BBN Butterfly and the ICL DAP respectively. A description of the Butterfly is given and the MIMD simulation on it is analysed in detail. Aspects of the system software of relevance to this simulation are presented and the programming practicalities are discussed. Timings are given for the molecular dynamics liquid SF6 simulation on the Butterfly, and a breakdown is given for the performance factors for this parallel computer. The rough estimate performance on this complete problem using a 44-processor machine was about 0.4 Mflops per processor.

We present a Monte Carlo analysis of the SU(2) finite-temperature deconfinement transition on a body-centered hypercubic lattice. The behavior of the transition temperature ${T}_{c}$ as a function of the lattice coupling \ensuremath{\beta} appears to deviate from the perturbative prediction of asymptotic scaling.

High statistics Monte Carlo Data in SU(2) lattice gauge theory are presented. At β = 2.6 and β = 2.7 large deviations from scaling are observed for Creutz ratios, when 124 and 244 lattice data are compared. There is a trend towards a restauration of asymptotic scaling with increasing β, which vanishes if at the higher value of β larger loops are considered than at lower β. The static qq̄-potential and an upper limit for the string tension are given.

On decrit la methode pour implanter l'algorithme de Monte Carlo pour calculer des boucles de Wilson et des lignes dans une theorie de jauge SU(2) sur un reseau hypercubique corps centre

The SU(2) string tension is obtained from measurements of Wilson loops on a ${6}^{4}$ bodycentered hypercubic lattice. A crude perturbative determination of $\ensuremath{\Lambda}$ indicates that the results are consistent with those of the hypercubic lattice. However, the $\ensuremath{\chi}(2)$ loop ratio is found to follow the asymptotic-freedom curve for a much larger range of ${g}_{0}$ than has ever been observed for any hypercubic actions. This strongly indicates that the bodycentered lattice may, for a given amount of computer run time, greatly increase the reliability of nonperturbative calculations.

For many arbitrary lattices with arbitrary $\mathrm{SU}(N)$ actions, it is easy to estimate the perturbative value of $\frac{{\ensuremath{\Lambda}}_{\mathrm{latt}}}{{\ensuremath{\Lambda}}_{\mathrm{MOM}}}$ without calculating any Feynman diagrams. This observation, first made by Creutz, is based on the fact that perturbative expansions of Wilson loop ratios can be trivially extracted from Monte Carlo data at large $\ensuremath{\beta}$. Here, we extend Creutz's results to general loop ratios including those of polygons and parallelograms encountered on nonstandard lattices. In particular, we analytically compute the lowest-order quantum corrections to these loop ratios, discuss which ratios are free from divergences, and give specific Monte Carlo examples.

We construct a chiral Lagrangian on a body-centered four-dimensional hypercubic lattice. A form of fermion doubling is observed in the continuum limit. However, because some of the spurious excitations do not propagate as particles, the resulting continuum field theory is not Lorentz invariant.

Monte Carlo techniques are used to calculate the average plaquette on a body-centered hypercubic lattice. Results are qualitatively similar to those previously obtained on the standard lattice but important quantitative differences are noted.

The ratio $\frac{{\ensuremath{\Lambda}}_{\mathrm{MO}}}{{\ensuremath{\Lambda}}_{\mathrm{latt}}}$ is computed for quantum chromodynamics (QCD) with massless fermions present. The result obtained, using the Wilson form of the lattice action, is $\frac{{\ensuremath{\Lambda}}_{\mathrm{MO}}}{{\ensuremath{\Lambda}}_{\mathrm{latt}}}=117.5$. We show how our methods can readily be extended to other forms of the action. Appendices give details of the technology of QCD perturbation theory on the lattice. Included are derivations of Feynman rules and Ward identities as well as general power-counting arguments and a discussion of the renormalization group.

We evaluate the fermionic contribution to $\frac{{\ensuremath{\Lambda}}_{\mathrm{latt}}}{{\ensuremath{\Lambda}}_{\mathrm{MO}}}$, up to the one-loop in weak-coupling lattice gauge theory, using direct numerical methods. The approach is much more straightforward than previous approaches and provides insight into the behavior of the theory for nonzero lattice spacing. The result we obtain in the limit of zero lattice spacing is in agreement with earlier calculations.

We compute analytically the logarithmic corrections to the photon propagator to order ${g}^{4}$ in massless quantum chromodynamics. With ${\ensuremath{\alpha}}_{c}=\frac{{g}^{2}}{4{\ensuremath{\pi}}^{2}}$ defined by momentum-space subtraction, we find that $\frac{\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons})}{\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})}={\ensuremath{\Sigma}}_{q}{{\ensuremath{\epsilon}}_{q}}^{2}(1+{\ensuremath{\alpha}}_{c}+K{{\ensuremath{\alpha}}_{c}}^{2}+\ensuremath{\cdots})$, where $K=\frac{463}{48}+(\frac{85}{36}\sqrt{3}){\mathrm{Cl}}_{2}(\frac{\ensuremath{\pi}}{3})\ensuremath{-}11\ensuremath{\zeta}(3)+[(\frac{2}{3})\ensuremath{\zeta}(3)\ensuremath{-}\frac{23}{36}]{n}_{f}=\ensuremath{-}2.193+0.162{n}_{f}$ for ${n}_{f}$ flavors of quark. The computation is done in momentum space using a novel generalization to $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions of the usual Chebyshev-polynomial expansion of Feynman propagators.

Order-${{\ensuremath{\alpha}}_{s}}^{2}$ corrections to the annihilation of ${e}^{+}{e}^{\ensuremath{-}}$ into hadrons are computed analytically. We briefly discuss the technique, which involves the extension to noninteger dimensions of Chebyshev expansions. In the energy range 15-30 GeV (five flavors) we find $R=3\ensuremath{\Sigma}{{e}_{Q}}^{2}{1+\frac{{\ensuremath{\alpha}}_{s}(q)}{\ensuremath{\pi}}\ensuremath{-}0.94{[\frac{{\ensuremath{\alpha}}_{s}(q)}{\ensuremath{\pi}}]}^{2}+\dots{}},$ where ${\ensuremath{\alpha}}_{s}$ is the momentum-space subtracted strong-coupling constant. Our result agrees with that of Dine and Sapirstein, and Chetyrkin, Kataev, and Tkachov.

Massless quantum chromodynamics cannot be renormalized on-shell; various possible off-shell renormalization prescriptions yield different definitions of a scale-dependent coupling constant $g$. We show how to relate physical predictions computed in different renormalization schemes. In particular, we compute the dimensionally regularized two- and three-point functions at the symmetric point in momentum space through one-loop order, and deduce the relation between ${g}_{min}$ defined by minimal subtraction and ${g}_{\mathrm{mom}}$ defined by momentum-space subtraction. We find that ${g}_{\mathrm{mom}}$ is fairly insensitive to which vertex one chooses to define it, and only weakly gauge dependent. ${g}_{min}$ is shown to depend strongly on the dimensional-regularization procedure, and can therefore differ quite dramatically from ${g}_{\mathrm{mom}}$. The scale dependence of $g$ is conventionally parametrized by a scale-invariant mass $\ensuremath{\Lambda}$; the ratio of $\ensuremath{\Lambda}$'s defined by any two renormalization schemes is a pure number which we show is exactly deducible from our one-loop results.

We relate two popular methods of renormalization; minimal subtraction and momentum-space subtraction. It is shown that $\frac{{\ensuremath{\Lambda}}_{\mathrm{mom}}}{{\ensuremath{\Lambda}}_{min}}=5.73$, where $\ensuremath{\Lambda}$ is the mass used to parametrize the quantum-chromodynamic running coupling constant. Perturbation expansions are compared in the two methods. Our results support the conjecture that momentum-space subtraction leads to better convergence and that, therefore, ${\ensuremath{\Lambda}}_{\mathrm{mom}}$ is the parameter which should be measured by experiments.

Quantum-chromodynamics radiative corrections to the vector-meson lepton width are discussed. These may modify the zeroth-order equation of Van Royen and Weisskopf, thereby leading to a significant suppression, by about a factor of 2, of the calculated value of $\ensuremath{\Gamma}$. Consequences for phenomenology are examined. In particular, a prediction is made for the width of ${\ensuremath{\Upsilon}}^{\ensuremath{'}}$, as well as for widths of heavier mesons.

We use ideas about quantum chromodynamics at large and small momenta to find a plausible explicit form for a $Q\overline{Q}$ potential. We fit the observed $s$-wave meson masses and predict the masses of bound states of yet heavier quarks.

We consider a Bethe-Salpeter kernel consisting of one gluon propagating between two dressed quark-gluon vertices. In order to derive the corresponding nonrelativistic potential to $O({(\frac{v}{c})}^{2})$ we find that it is necessary to choose a special gauge in which the time-time component of the propagator is instantaneous (to that order). The resulting Fermi-Breit potential including an anomalous magnetic moment is presented and compared with previous results.

The running coupling constant of quantum chromodynamics ${\ensuremath{\alpha}}_{s}({q}^{2})$ is obtained for all ${q}^{2}$ by integrating the renormalization-group equation. The $\ensuremath{\beta}$ function in the asymptotic- freedom region is given by perturbation theory through order ${g}^{5}$ and at large coupling by the string model with string tension related to the Regge slope ${\ensuremath{\alpha}}^{\ensuremath{'}}$. We incorporate these features into a Pad\'e approximant to the $\ensuremath{\beta}$ function thereby obtaining it for all $g$. The constant of integration $\ensuremath{\Lambda}$ of the renormalization-group equation is chosen to be about 500 MeV, as required by deep-inelastic phenomenology. ${\ensuremath{\alpha}}_{s}$ is thus completely determined by ${\ensuremath{\alpha}}^{\ensuremath{'}}$, $\ensuremath{\Lambda}$, and the first two terms of the $\ensuremath{\beta}$ function. The resulting charmonium and $\ensuremath{\Upsilon}$ spectroscopy is in excellent agreement with experiment. In particular the ${\ensuremath{\Upsilon}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\Upsilon}$ mass difference is forced to be nearly equal to the ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\psi}$ mass difference. In addition, it is shown that the structure of ${\ensuremath{\alpha}}_{s}(q)$ signals the presence of instantons.

It has recently been predicted by De R\'ujula et al. that $m({D}^{+})\ensuremath{-}m({D}^{0})\ensuremath{\sim}15$ MeV. The purpose of this Letter is to criticize this prediction and to examine in detail the mechanism responsible for meson mass splittings. It is concluded that electromagnetic splittings of hadrons cannot reliably be estimated using the present atomic models of hadrons. New terms are probably needed in the electromagnetic part of the potential.