The super-heat-kernel expansion and the renormalization of the pion-nucleon interaction

A recently proposed super-heat-kernel technique is applied to SU(2)(L) x SU (2)(R) heavy baryon chiral perturbation theory. A previous result for the o ne-loop divergences of the pion-nucleon system to O(p(3)) is confirmed, giv ing at the same time an impressive demonstration of the efficiency of the n ew method. The cumbersome and tedious calculations of the conventional appr oach are now reduced to a few simple algebraic manipulations. The present c omputational scheme is not restricted to chiral perturbation theory, but ca n easily be applied or extended to any (in general non-renormalizable) theo ry with boson-fermion interactions.