Don Weingarten

Hamiltonian evolution for the hybrid Monte Carlo algorithm

We discuss a class of reversible, discrete approximations to Hamiltons equations for use in the hybrid Monte Carlo algorithm and derive an asymptotic formula for the step-size-dependent errors arising from this family of approximations. For lattice QCD with Wilson fermions, we construct several different updates in which the effect of fermion vacuum polarization is given a longer time step than the gauge fields self-interaction. On a 44 lattice, one of these algorithms with an optimal choice of step size is 30% to 40% faster than the standard leapfrog update with an optimal step size.

Hadronic coupling constants in lattice gauge theory

Abstract We describe an efficient method for calculating hadronic three-point functions in lattice gauge theory. We use the method to calculate the π-nucleon coupling constant the the coupling constants for the hadronic decays of the ρ and K ∗ mesons and the Δ, Σ ∗ , and Ξ ∗ baryons.

Hadron mass predictions of the valence approximation to lattice QCD

We evaluate the infinite-volume, continuum limits of eight hadron mass ratios predicted by lattice QCD with Wilson quarks in the valence (quenched) approximation. Each predicted ratio differs from the corresponding observed value by less than 6%.

Hadron wave functions in lattice QCD

Coulomb gauge quark-antiquark wave functions for the pion and the rho are calculated in the valence approximation on a lattice 83 × 16. We use gauge group SU(2) at β of 2.431 corresponding to an inverse lattice spacing of 1100 ± 100 MeV. The wave functions fall off significantly over the size of the box, are rotationally invariant except at the boxs boundary, and are nearly independent of the lagrangian quark mass.

Scalar quarkonium and the scalar glueball

Abstract Valence approximation glueball mass and decay calculations support the identification of fJ(1710) as the lightest scalar glueball. An alternate glueball candidate is f0(1500). I present evidence for the identification of f0(1500) as ss quarkonium.

Algorithms for Monte Carlo calculations with fermions

We describe a fermion Monte Carlo algorithm due to Petcher and the present author and another due to Fucito, Marinari, Parisi and Rebbi. For the first algorithm we estimate the number of arithmetic operations required to evaluate a vacuum expectation value grows as N11/mq on an N4 lattice with fixed periodicity in physical units and renormalized quark mass mq. For the second algorithm the rate of growth is estimated to be N8/m2q. Numerical experiments are presented comparing the two algorithms on a lattice of size 24. With a hopping constant K of 0.15 and β of 4.0 we find the number of operations for the second algorithm is about 2.7 times larger than for the first and about 13 000 times larger than for corresponding Monte Carlo calculations with a pure gauge theory. An estimate is given for the number of operations required for more realistic calculations by each algorithm on a larger lattice.

Absence of Species Replication for a Class of Disordered Fermion Couplings

Abstract We present a disordered coupling scheme for free lattice fermions in two-dimensional spacetime. The theory is chirally invariant for a fermion mass of zero but does not lead to species replication and does not incorporate any long-range couplings. The fermion action breaks reflection positivity, the condition normally used to prove the existence of a self-adjoint hamiltonian for euclidean lattice field theories. Potential species replicas and states breaking reflection positivity decouple from processes which occur on a physical length scale because their wave functions become localized in the disordered lattice in somewhat the same way that electrons can become localized in a disordered solid.

Complex probabilities on R(N) as real probabilities on C(N) and an application to path integrals.

We establish a necessary and sufficient condition for averages over complex-valued weight functions on R(N) to be represented as statistical averages over real, non-negative probability weights on C(N). Using this result, we show that many path integrals for time-ordered expectation values of bosonic degrees of freedom in real-valued time can be expressed as statistical averages over ensembles of paths with complex-valued coordinates, and then speculate on possible consequences of this result for the relation between quantum and classical mechanics.

Volume dependence of the valence Wilson fermion mass spectrum

Abstract We present hadron mass spectrum results for valence Wilson fermions obtained from simulations on the GF11. We performed high statistic runs on three physical volumes, 8 3 × 32, 16 3 × 32, and 24 3 × 32, all with the same coarse lattice spacing, β = 5.7. We see no systematic difference between our 8 3 and 16 3 results at the large quark masses we could simulate on 8 3 . Our 16 3 and 24 3 results also agree at the small quark masses we simulated on these larger volumes.

Monte Carlo algorithms for QCD

Abstract We present a classification of the Monte Carlo algorithms which have been suggested for QCD including the full effect of fermions, and discuss which of these are likely to be the most efficient.