Field transformations and simple models illustrating the impossibility of measuring off-shell effects - art. no. 034003

In the context of simple models utilizing field transformations in Lagrangi an field theories we discuss the impossibility of measuring off-shell effec ts in nucleon-nucleon bremsstrahlung, Compton scattering, and related proce sses. Our aim is to illustrate the general results using simple and familia r models. To that end we introduce a simple phenomenological Lagrangian des cribing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon a mplitude as well as the photon-nucleon vertex. As a result we obtain a clas s of equivalent Lagrangians, generating identical S-matrix elements, of whi ch the original Lagrangian is but one representative. We make use of this p roperty in order to show that what appears as an off-shell effect in an S-m atrix element for one Lagrangian may originate in a contact term from an eq uivalent Lagrangian. By explicit calculation we demonstrate for the case of nucleon-nucleon bremsstrahlung as well as nucleon Compton scattering the e quivalence of observables from which we conclude that off-shell effects can not in any unambiguous way be extracted from an S-matrix element. Finally, we also discuss some implications of introducing off-shell effects on a phe nomenological basis, resulting from the requirement that the description of one process be consistent with that of other processes described by the sa me Lagrangian.