The Pion – Nucleon Interaction as an Effective Field Theory

After a brief survey of effective field theories, the linear σ model is discussed as a prototype of an effective field theory of the standard model below the chiral–symmetry–breaking scale. Although it can serve as a toy model for the pion–nucleon interaction, the linear σ model is not a realistic alternative to chiral perturbation theory. The heavy–baryon approach to chiral perturbation theory allows for a systematic low–energy expansion of Green functions and amplitudes with baryons. The chiral–invariant renormalization of the effective field theory for the pion–nucleon system to O(p 3) in the chiral expansion is reviewed.