Jeffrey E. Mandula

Quark pair condensation and chiral symmetry breaking in QCD

If the effective qq interaction strength due to gluon exchange becomes at least moderately strong beyond some distance g2/4π > 98, the perturbative vacuum becomes unstable to the creation of color singlet qq pairs, which indicates that the true vacuum contains a condensate of such pairs. We analyze the condensation by a coherent state variational procedure modeled after the BCS superconductor, and show that this method is equivalent to a self-consistent Hartree-Fock approximation to the Schwinger-Dyson equation for the quark propagator. The condensate leads to a spontaneous breakdown of chiral symmetry in the manner discussed by Nambu and Jona-Lasinio. The massive pseudoparticles with quark quantum numbers are identified with the “constituent” quarks.

Efficient gauge fixing via overrelaxation

Abstract Overrelaxation is shown to be an effective technique for fixing the gauge in lattice gauge theories.

REPRESENTATIONS OF THE ROTATION REFLECTION SYMMETRY GROUP OF THE FOUR-DIMENSIONAL CUBIC LATTICE

Abstract The structure and representations of the rotation reflection symmetry group of the four-dimensional cubic lattice are described. Their connections with the representations of the three-dimensional lattice rotation reflection group, and with the representations of the continuous O(3) and O(4) groups are given.

Color screening by a Yang-Mills instability

Abstract The Coloumb field set up by a classical Yang-Mills particle is shown to be unstable above a critical coupling strength. The instability is related to color screening and represents a classical phase transition. Possible connections with the confinement problem are discussed.

COVARIANT LATTICE GLUEBALL FIELDS

Abstract Fields for the creation and annihilation of gluons and glueballs, which transform irreducibly under the four-dimensional lattice rotation reflection and charge conjugation symmetry groups, are defined and discussed. The fields reduce in the zero lattice spacing limit to conventional continuum operators of definite spin, parity, and charge comjugation.

The gluon propagator at finite temperature

Abstract The Landau gauge gluon propagator at finite temperature above and below the deconfinement transition is measured using lattice Monte Carlo simulation. The color electric and magnetic masses are determined. The most striking result of the calculation is that the time component of the gluon field appears to acquire a vacuum expected value in the deconfined region.

THE PION IN QCD

Abstract A model for chiral symmetry breaking in QCD patterned on the BCS theory of superconductivity is given.

Total charge screening

Abstract Solutions of classical massless scalar electrodynamics with a large external charge which exhibit total charge screening, that is, in which the charge in the field exactly neutralizes the external charge, are found. These solutions have lower energy than the unscreened Coulomb potential. The relation to the color screening problem in QCD is discussed.

A MODEL FOR CHIRAL SYMMETRY BREAKING IN QCD

Abstract A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M Q , the constituent quark mass ƒ π the pion decay coupling, 〈 u u〉 , the constituent quark loop density, μ π 2 / m q , the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈 r 2 〉 π , the pion electromagnetic charge radius squared.

Pion Properties in {QCD}

Abstract A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of the pion form factor. The pion charge radius is explicitly computed.