Lattice Gauge Calculations Research Articles

Investigations On the Full and Reduced Salpeter Equation for the Quark-Anti Quark Bound States

The solutions for both the full Salpeter equation and the reduced Salpeter equation for the quark-anti quark bound states are investigated. General solutions and the solutions in the nonrelativistic approximation are discussed. Differences between two kinds of Salpeter equations are emphasized. It is especially noted that the observed mass splitting could be accounted for by using the full salpeter equation with a smaller vector Coulomb potential -α/r, where , which was obtained in very recent lattice gauge calculations and might be associated with the zero-point transverse fluctuations of the relativistic string.

Discretized light-cone quantization: The massless and the massive Schwinger model.

The method of discretized light-cone quantization (DLCQ), recently proposed for obtaining nonperturbative solutions to field theories, is applied to quantum electrodynamics in one space dimension (QED/sub 2/). The spectrum of invariant masses and the eigenfunctions of the light-cone Hamiltonian are calculated; i.e., the bound-state problem is solved for all values of the coupling constant. For very strong coupling (Schwinger model proper) DLCQ reproduces one to one the known exact solutions. For nonvanishing fermion mass (massive Schwinger model) the results of DLCQ agree with earlier work and in particular with a lattice gauge calculation.

Quark vacuum polarization and the Lüscher term.

The L\"uscher term found in the QCD string model and in Monte Carlo lattice gauge calculations is significantly modified by vacuum polarization due to light-quark loops. This modification improves agreement with experiment.

Lattice gauge calculation in particle theory

There are many problems in particle physics which cannot be treated analytically, but are amenable to numerical solution using today's most powerful computers. Prominent among such problems are those encountered in the theory of strong interactions, where the resolution of fundamental issues such as demonstrating quark confinement or evaluating hadronic structure is rooted in a successful description of the behaviour of a very large number of dynamical variables in non-linear interaction. This paper briefly outlines the mathematical problems met in the formulation of the quantum field theory for strong interactions, the motivation for numerical methods of resolution and the algorithms which are currently being used. Such algorithms require very large amounts of memory and computation and, because of their organized structure, are ideally suited for implementation on mainframes with vectorized architecture. While the details of the actual implementation will be covered in other contributions to this conference, this paper will present an account of the most important physics results obtained up to now and will conclude with a survey of open problems in particle theory which could be solved numerically in the near future.

Conference summary — lattice gauge theory and heavy-ion collisions

This conference summary consists of three parts. First, a primer, in the form of questions and answers, on lattice gauge theory is presented to familiarize nuclear physicists and experimentalists involved with heavy-ion collisions with the basics of this field. Second, the contributions to the conference on the thermodynamics of gauge fields, computer simulation at non-zero chemical potential and the inclusion of dynamical massless quarks into lattice gauge calculations, are reviewed. And third, the lack of adequate computer facilities needed to improve the present generation of calculations is discussed and a proposal for a Center for Heavy-Ion Simulations is sketched to solve the dilemma.

Quarks in nuclei

Some features of quark degrees of freedom in nuclei are discussed in the light of recent developments in QCD. The principal aim of this talk is to propose, and give a tentative support to, the notion that one can study through nuclear matter different facets of the vacuum structure implied by quantum chromodynamics (QCD) . This will be done using the recent (exciting) results obtained in particle physics, in particular lattice gauge calculations. Relevance of this aspect of problem to quark degrees of freedom as well as meson degrees of freedom in nuclei will be discussed.

The problem of the displaced scalar meson states

It is argued that the absence of qq̄ scalar mesons in the 1 to 1.2 GeV region would pose serious problems for the non-relativistic quark model description of the spin-dependence of both meson and baryon spectra. Since the lattice gauge calculations of Hamber and Parisi predict that the light qq̄ scalar mesons lie below the axial vector mesons in the same multiplet, this issue may have wider implications.