Field transformations and simple models illustrating the impossibility of measuring off-shell effects

Details Field transformations and simple models illustrating the impossibility of measuring off-shell effects Field transformations and simple models illustrating the impossibility of measuring off-shell effects

1999-09-30

arxiv.org/abs/nucl-th/9909076v1

Phys.Rev. C62 (2000) 034003

Physics

Nuclear Physics

Nuclear Theory

19 pages, Latex, using RevTex

Scientific paper

10.1103/PhysRevC.62.034003

In the context of simple models illustrating field transformations in Lagrangian field theories we discuss the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung, Compton scattering, and related processes. To that end we introduce a simple phenomenological Lagrangian describing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon amplitude as well as the photon-nucleon vertex. As a result we obtain a class of equivalent Lagrangians, generating identical S-matrix elements, of which the original Lagrangian is but one representative. We make use of this property in order to show that what appears as an off-shell effect in an S-matrix element for one Lagrangian may originate in a contact term from an equivalent Lagrangian. By explicit calculation we demonstrate for the case of nucleon-nucleon bremsstrahlung as well as nucleon Compton scattering the equivalence of observables from which we conclude that off-shell effects cannot in any unambiguous way be extracted from an S-matrix element. Finally, we also discuss some implications of introducing off-shell effects on a phenomenological basis, resulting from the requirement that the description of one process be consistent with that of other processes described by the same Lagrangian.

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