Compton scattering by a pion and off-shell effects.

We consider Compton scattering by a pion in the framework of chiral perturbation theory. We investigate off–shell effects in the s– and u–channel pole diagrams. For that purpose we perform a field transformation which, in comparison with the standard Gasser and Leutwyler Lagrangian, generates additional terms at order p4 proportional to the lowest–order equation of motion. As a result of the equivalence theorem the two Lagrangians predict the same Compton scattering S–matrix even though they generate different off–shell form factors. We conclude that off–shell effects are not only model– dependent but also representation–dependent. 13.60.F, 11.30.R, 13.40.G Typeset using REVTEX ∗Address after Sept. 1, 1994: Institut für Kernphysik, Johannes Gutenberg–Universität, J. J. Becher–Weg 45, D–55099 Mainz, Germany.