Strong Interactions at Low Energy

This is a revised version of a talk given at the Chiral Dynamics Workshop at M.I.T., July 25, 1994. It reports results in three areas: (1) The isospin-violating interactions between one non-relativistic nucleon and any number of soft pions can be summarized in a single term in the effective chiral Lagrangian, with no unknown parameters. (2) With D'Hoker, it has been shown that the terms in the Lagrangian for an effective field theory with symmetry $G$ spontaneously broken to $H$, that are not the integrals of $G$-invariant Lagrangian densities, are in one-to-one correspondence with the generators of $H_5(G/H,R)$. (3) If we assume that the nucleon is connected by successive one-pion transitions only to a tower of narrow baryon states with $T=J=1/2,3/2,\dots,N_c/2$, then the Adler-Weisberger and superconvergence relations tell us (for any $N_c$) that (a) the tower states are degenerate, and (b) the one-pion transition amplitudes between these states generate the {\em uncontracted} algebra of $SU(4)\times O(3)$.