We derive a master formula for chiral SU(2) x SU(2) breaking, based on
the Veltman-Bell equations and the Peierls-Dyson relation. Our approa
ch does not rely on the use of the soft pion limit or an expansion aro
und the chiral limit, and yields exact results for on-shell pions. Thr
eshold theorems for pi N --> pi N, gamma N --> pi N, pi N --> pi pi N,
gamma N --> gamma pi N, gamma N --> pi pi N and pi N --> pi gamma N a
re recovered, and corrections to them are given. The reactions pi -->
e nu gamma, pi --> e nu e(+)e(-), gamma pi --> gamma pi and gamma gamm
a --> pi pi are also discussed. A general formula for pi pi scattering
and a new one loop effective action are obtained. The new effective a
ction reproduces the KSFR relation, and yields specific estimates for
the pion polarisabilities. A detailed comparison with baryon-free chir
al perturbation theory to one loop is made. An extension of our effect
ive action to two loops is outlined. (C) 1996 Academic Press, Inc.