  Applications imposing SU(3) chiral symmetry on non-relativistic field theory
are considered. The first example is a calculation of the self-energy shifts of
the spin-3/2 decuplet baryons in nuclear matter, from the chiral effective
Lagrangian coupling octet and decuplet baryon fields. Special attention is paid
to the self-energy of the delta baryon near the saturation density of nuclear
matter. We find contributions to the mass shifts from contact terms in the
effective Lagrangian with coefficients of unknown value. As a second
application, we formulate an effecive field theory with manifest SU(2) chiral
symmetry for the interactions of K and eta mesons with pions at low energy.
SU(3) chiral symmetry is imposed on the effective field theory by a matching
calculation onto three-flavor chiral perturbation theory. The effective
Lagrangian for the pi-K and pi-eta sectors is worked out to order Q^4; the
effective Lagrangian for the K-K sector is worked out to order Q^2 with contact
interactions to order Q^4. As an application of the method, we calculate the KK
s-wave scattering phase shift at leading order and compare with chiral
perturbation theory. We conclude with a discussion of the limitations of the
approach and propose new directions for work where the matching calculation may
be useful.
