4 Almost all nonperturbative studies in relativistic quantum field theory employ a Euclidean Metric. A Euclidean metric was used in writing Eq. (1.8). Appendix A provides some background and describes the Euclidean conventions employed herein.

We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading non-analytic behaviour (and hence the most rapid variation in the region of light quark mass), we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.

The properties of the kaon, $K$, and antikaon, $\kbar$, in nuclear medium are studied in the quark-meson coupling (QMC) model. Employing a constituent quark-antiquark (MIT bag model) picture, their excitation energies in a nuclear medium at zero momentum are calculated within mean field approximation. The scalar, and the vector mesons are assumed to couple directly to the nonstrange quarks and antiquarks in the $K$ and $\kbar$ mesons. It is demonstrated that the $\rho$ meson induces different mean field potentials for each member of the isodoublets, $K$ and $\kbar$, when they are embedded in asymmetric nuclear matter. Furthermore, it is also shown that this $\rho$ meson potential is repulsive for the $K^-$ meson in matter with a neutron excess, and renders $K^-$ condensation less likely to occur.Comment: Latex, 11 pages, 4 Postscript figures, a few typos which can be important for an interpretation (but not reflected in the results) are corrected, as published in (E) Phys. Lett. B 436 (1998) 45

Consideration of the analytic properties of pion-induced baryon self-energies leads to new functional forms for the extrapolation of light baryon masses. These functional forms reproduce the leading non-analytic behavior of chiral perturbation theory, the correct non-analytic behavior at the N π threshold and the appropriate heavy-quark limit. They involve only three unknown parameters, which may be obtained by fitting to lattice data. Recent dynamical fermion results from CP-PACS and UKQCD are extrapolated using these new functional forms. We also use these functions to probe the limit of applicability of chiral perturbation theory to the extrapolation of lattice QCD results.