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We have studied lattice QCD with an additional, irrelevant 4-fermion interaction having a U (1) × U (1) chiral symmetry, at finite temperatures. Adding this 4-fermion term allowed us to work at zero quark mass, which would have otherwise been impossible. The theory with 2 massless staggered quark flavours appears to have a first order finite temperature phase transition at N t = 4 for the value of 4-fermion coupling we have chosen, in contrast to what is expected for 2-flavour QCD. The pion screening mass is seen to vanish below this transition, only to become massive and degenerate with the σ (f 0 ) above this transition where the chiral symmetry is restored, as is seen by the vanishing of the chiral condensate.

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We have investigated several models of q -q binding in light-quark mesons using the Bethe-Salpeter (BS) equation in the instantaneous approximation. These were considered with regard to their ability to reproduce three essential features of the light-quark meson spectroscopy: the existence of light pseudoscalars, the linearity of Regge trajectories, and the smallness of spin-orbit splittings. This study has led us to reject both the hypothesis of a vector and of a scalar confining potential. Moreover, it has been shown that the BS kernel has to contain a chiral-symmetry-breaking part in order to accommodate the observed spin-orbit splittings. This in turn implies that the BS kernel has to depend on the mass (M) of the bound state itself in order to maintain compatibility with the Goldstone theorem. Under these circumstances we were able to produce a model based on a vector confining potential complemented by an M-dependent reversed spin-orbit coupling which satisfies the three requirements mentioned above. In all these considerations the spontaneous breaking of chiral symmetry plays an essential role not only because of its direct implications on the spectrum but also because it determines the kinetic energy and the quark form factors to be used in the BS equation.

We introduce a new class of actions for staggered quarks in lattice QCD which significantly reduce flavour symmetry violations in the pion mass spectrum.An action introduced by the MILC collaboration for the same purpose is seen to be a special case. We discus how such actions arise from a systematic attempt to reduce flavour symmetry violations in the weak coupling limit. It is shown that for quenched lattice QCD at 6/g 2 = 5.7, representative actions of this class give a considerable reduction in flavour symmetry violation over the standard staggered action, and a significant reduction over what is achieved by the MILC action.